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Received N.QV...1.4..1.91.1 

^cessions No. & f Z Book m _/ 



J. S. AMES, PH.D. 














Entered at Stationers'' Hall, London. 

Radiation and Absorption. 
W. P. i 

\ \ 


THE attempt of Prevost to explain the experiments of Pictet, 
of the apparent concentration of cold at the focus of a mirror, 
without attributing the quality of radiation to cold, as assumed 
by Pictet, lead him to the enunciation of the very important 
principle which he called the movable equilibrium of heat, now 
designated as the theory of exchanges. Prevost, who was a dis- 
ciple of le Sage, and who had issued, with many additions, his 
memoirs, assumed, in addition to a corpuscular fluid caloric, a 
free corpuscular radiant caloric, the equal interchange of which 
between neighboring free spaces, constituted heat equilibrium. 
Any interference with this equilibrium will be reestablished by 
the inequalities of the exchanges. On this principle he was able 
to explain the apparent concentration of cold and also to show 
the inadmissibility of cold as an agent susceptible of radiation. 
He was careful, however, to fortify his principle by showing that 
the same results would follow on the then distrusted hypothesis 
of undulatory exchanges, which has been adopted by his suc- 
cessors. Later experimenters, particularly Leslie and De la 
Provastaye and Desains, confirmed the theory and also showed 
in many instances quantitative relations between radiation and 
absorption. But the most important advance was made by Bal- 
four Stewart in establishing, not only a quantitative relation, 
but also a qualitative or selective one. By the introduction of 
his ingenious idea of an impervious radiating inclosure he 
demonstrated the equality between the emissive and the absorp- 
tive power of any wave length. We owe to Kirchhoff, however, 
the first rigorous proof of the celebrated law (usually designated 
on the Continent as KirchhofFs law) of the emission and absorp- 
tion of light and heat, and the application of the same by both 
Kirchhoff and Bunsen to Spectrum Analysis. The radiation 
of solids and liquids and gases follows the law exactly when the 
conditions upon which he founded it are rigorously fulfilled, 
namely, the complete transformation from one to the other of 



radiant energy and their intrinsic heat. "We now know that 
most radiations from gases are not exclusively thermal, but that 
the substances, cited by Kirchhoff and Bunsen, also give off so 
called chemical and electrical and fluorescent radiations which 
Kirchhoff excluded in the proof of his law. In fact none of the 
gases giving line spectra at temperatures heretofore used do so 
by simple thermal radiation, but essentially by luminescent 
actions (chemical, electrical, and photogenic), so that we cannot, 
in general, apply the law of Kirchhoff of the proportionality 
between radiation and absorption to either terrestrial or celes- 
tial substances. In these cases the principle of resonance usually 
holds, since in luminescence the radiation of line spectra is 
accompanied by selective absorption of the same spectral lines, 
so that the law may be used qualitatively, which is in ftict the 
way Kirchhoff and Bunsen actually attempted to confirm it. 
The formulation of the complete law for radiations of a Hack 
body is only given in part by Kirchhoff. The formula of Wien, 
and more particularly the most recent one of Planck, deduced 
on theoretical grounds, approximates closely the latest observa- 
tions on a black body at different temperatures and over differ- 
ent wave lengths. 

University of Nebraska. 




Preface ' . v 

On the Equilibrium of Heat. Pierre Prevost .... 1 
Treatise on Radiant Heat (Selections). Pierre Prevost . . 15 

Biographical Sketch of Prevost 20 

An account of some Experiments on Radiant Heat, involv- 
ing an extension of Prevost's Theory of Exchanges. 

By Balfour Stewart 21 

Researches on Radiant Heat. Second Series. By Balfour- 

Stewart . . 51 

Biographical Sketch of Stewart. ... . . 72 

On the Relation between the Emissive and the Absorptive 
Power of Bodies for Heat and Light. By G. R. Kirch- 

hoff -73 

Biographical Sketch of Kirchhoff ... . 97 

Chemical Analysis by Spectral Observations by G. Kirch- 126 
hoff and R. Bunsen ... .... 99 

Biographical Sketch of Bunsen . . 126 

Bibliography 127 

Index , ..... 129 





Journal de Physique, vol. 38, pp. 314-322. Paris, 1791. 



Outline of the Proposed Discussion 3 

Theory of the Equilibrium of Heat ..... 4 

Rupture of the Equilibrium between two Portions of Space 6 

Phenomenon of Reflection of Cold . . . . . 7 

Exclusion of an Independent Explanation . . . . 9 
Supplementary Remarks on Radiant Heat . . .11 

Discussion of /Several Discrete Fluids . " . . . . 12 



I PROPOSE to analyse and fix with precision the sense of the 
word equilibrium applied to such a fluid as heat. This idea is 
not exactly defined in the theories which leave questions rela- 
tive to the nature of this element undecided. If there is any 
doubt that heat is material, if there is no explanation concern- 
ing the contiguity or the noncontiguity of molecules of heat, 
concerning their mobility or their immobility, the kind of 
motion, vibratory or translatory, which is attributed to them, * 
it is impossible to arrive at exact and complete ideas of their 
equilibrium. It results from this that every phenomenon which 
depends, not upon any equilibrium whatever but upon a spe- 
cific kind of equilibrium, remains entirely unexplained. And 
as the imagination determines to some extent, notwithstanding, 
that which reason wishes to leave undetermined, the true 
causes are lost sight of, and vain hypotheses are arbitrarily 
preferred because they are suitable in certain respects and fav- 
orable to first appearances. 

I will not waste time in discussing the different natures 
assigned to heat by various physicists. The true constitution" 
of this fluid is connected with the theory of discrete fluids, now 
known, although it has not been published by its author. For 
its development and proof I refer to what M. DeLuc has said 
of it both in his " Idees sur la meteorologie" and in his letters 
published successively in this Journal: also what I have said of 
it myself in my essay upon I'origine des forces magnetiques. 
Assuming then the principles of this theory, I shall merely recall 
them, and use them to establish true ideas on the equilibrium 
of heat. 

I shall afterwards make the application of this theory of the 
equilibrium of heat to a very remarkable phenomenon which I 
consider inexplicable without it. This is the phenomenon of 
the reflection of cold. It has been observed by M. Pictet, who 



has described it in detail in his essai sur le feu. This learned 
scientist, with whom I have old and valued bonds of friendship, 
does not at all disapprove of the discussion which I am under- 
taking although it tends to indicate some inadequacy in the 
explanation which he, himself, has given to this phenomenon. 
It will be seen elsewhere by what I shall say of it, that a com- 
plete explanation, such as the theory of M. le Sage furnished, 
does not enter into the plan which M. Pictet has proposed. I 
will discuss this phenomenon then, very freely. I shall show that 
it explains itself without any effort, by the true theory of dis- 
crete fluids. I shall also prove that it is not explained at all by 
the imperfect theories to which physicists commonly limit 
themselves. I shall close this memoir with two remarks which 
have some connection with this subject, without being directly 
related to it. 



Heat is a discrete fluid. Its elasticity consists in its expau- 
^ sive force. And this is the effect of the movement of its 
particles. This movement is caused by the impulse of a much 
more subtile fluid whose effect upon its particles is determined 
to a certain extent by their form. It is so swift that when heat 
NO is freed its translation from one place to another appears in- 
stantaneous. It is also sensibly rectilinear, so that perfectly 
free heat partakes, as far as the movement of its particles is 
concerned, of all the properties of light, at least so far as our 
senses can determine in the limited experiments which have 
thus far been performed. 

A discrete fluid whose particles radiate like those of light, 
may be confined by barriers, but may not be confined by an- 
other radiant fluid nor, in consequence, by itself. For it is 
necessary to conceive of all these fluids as very rare, as having 
many more void intervals than full ones in the space which 
they occupy. Light does not stop the passage of light. If this 
solar emanation is so dense that two luminous currents cannot 
cross each other without being interrupted, the innumerable 
crossings and reflections which they experience will destroy 
entirely its rectilinear direction, and light will lose to our eyes 



all its properties which depend upon this direction. What is 
true of this fluid is true of all radiant fluids. Radiant heat 
passes through heat, which upon the earth is present in all 
places, and since it produces no sensible perturbation, it is nec- 
essary that these particles should be separated by intervals great 
relatively to their diameters. It is certain that free radiant 
heat is a very rare fluid, the particles of which almost never 
collide with one another and do not disturb sensibly their mu- 
tual movements. 

In conforming to physical hypotheses, one says ordinarily 
that heat is coercible by itself : that two contiguous portions of 
heat have a mutual relation when their temperatures are equal 
(or as M. Volta has said, when their tensions are the same). 
These expressions are exact, only in so far as they define an ap- 
pearance. In reality the heat of any portion cannot arrest that 
of another. These two heats give each other mutually free 
passage. It would then be wrong for one to conclude from 
these expressions that two portions of contiguous heat restrain 
each other mutually, as two bent springs stayed against 
one another, or as two masses of hair which repel each other 
by their elasticity. 

But in what does the equilibrium of these two portions of 
contiguous heat consist ? In order to answer this question 
clearly, I will suppose the two portions to be enclosed in an 
empty space, terminated on all sides by impenetrable walls. 
One may represent two cubes applied by one of their faces, 
forming in consequence a rectangular parallelepiped perfectly 
hollow, of which the six faces are of the same matter, absolutely 
solid and without pores. The two portions which I consider 
are, in this example, the two applied cubes. The heat occupy- 
ing the interior of this space moves freely there, and as- 
suredly one can see no reason why it should pass with less 
facility across the boundary of the two portions than across 
every other section of this space. There are then continual ex- 
changes from one portion to another, and one can affirm (in 
consideration of the number of particles and their continual 
motion) that at each observable instant the state and quantity 
of the heat in each portion are constant. There is then no 
ceasing of the different particles, which are found at any one 



place, but their number and their meau distance in each 
portion are constant. Concerning their speed, as it is in the 
same free fluid (consider the constant nature of the cause 
which produces and renews it continually), it is clear that it 
does not change : and I shall leave it out of the question, since 
at the present moment I consider only free radiant heat. 

At all times that both portions of the space are found in the 
circumstances which I have just described, the heat between 
them is in a state of equilibrium. This signifies that the 
phenomena which manifest their existence remain the same : 
that if these phenomena change in the same manner and in the 
same quantity in the two portions, the equilibrium in question 
will not be disturbed. This would occur if one should remove 
from the total space, which we are considering, a certain 
aliquot part of all the heat found there, or indeed if this 
aliquot part should be added. The identity of the phenomena 
which implies the equilibrium of heat between these two por- 
tions of space is a relative identity, which, as one can see, may 
exist whatever may be the difference or the absolute in- 

Let us now suppose that into one of the two portions of space 
(which I will represent constantly by the two adjoining cubes) 
one passes suddenly some new heat ; for example, one tenth of 
all that which is contained in this portion. This heat, in- 
stantly placed in motion, spreads immediately throughout all 
the space where it can penetrate freely. Thus the exchanges 
between the two portions would be unequal. One would send to 
the other eleven particles, while the latter would return only 
ten. This state causes a rupture of the equilibrium between 
the two portions. 

By reason of the unequal exchanges one may conceive that 
the equality would be reestablished. Thus the rupture of the 
equilibrium restores very quickly the equilibrium between two 
portions of free heat. 1 

1 Suppose that the densities of the heat in our two cubes are as the 
numbers 1 and 2 (i. e., that one is twice as hot as the other) : suppose 
further that in one second there passes from the one cube to the other a 
number of igneous particles which on the whole are as 1 to 10 (so that 
during this short time there is exchanged one tenth of all the heat). 



Absolute equilibrium of free heat is the state of this fluid in 
a portion of space which receives as much as it allows to 
escape it. 

Relative equilibrium of free heat is the state of this fluid in 
two portions oi' space which receive from each other equal 
quantities of heat, and which are, moreover, in absolute equilib- 
rium, or experience changes precisely equal. 

The heat of several portions of space at the same temperature 
and near each other is at once in the two kinds of equilibrium. 
If one should change the temperature of all the space at the 
same time, it would destroy the absolute equilibrium, but not 
the relative equilibrium. Should the temperature of one or 
of several portions be altered without affecting all, each kind 
of equilibrium would be destroyed. 

If the cause which throws out or which absorbs the heat of 
any portion is an instantaneous cause, after the action of this 
cause the relative equilibrium reestablishes itself incessantly 
by means of unequal exchanges. And after this reestablish- 
ment the absolute equilibrium remains destroyed, that is to 
say, the temperature of the place is changed. 

If, on the contrary, the cause is permanent, that is to say, if 
there is opened in any one of the portions of this space a source 
or a sink which gives out or which absorbs heat incessantly, rela- 
tive equilibrium tends to establish itself, but does not reestablish 
itself entirely during the action of the cause, and absolute 
equilibrium is constantly destroyed. 



Let us represent two spherical concave mirrors opposite to 
each other on their axes, and let us suppose placed at their foci 

After seven seconds the ratio of the densities of the heat in the two 
cubes will be as 5 to 6. After fourteen seconds, these densities will be 
as 28 to 29, i. e., very nearly equality : the equilibrium will appear 

I take this result from a calculation of M. le Sage thirty years since in 
the case of discrete fluids different from heat. 



two bodies precisely equal and similar and of the same sub- 
stance, which JL will call the two focal bodies. 

To simplify this I will suppose, (1) that all the space where 
the apparatus is immersed is absolutely cold and receives heat 
only from part of the two focal bodies, (2) that these are hot 
and give out radiant heat continuously, (3) that the mirrors re- 
flect the heat but do not absorb it. 

With these conditions, it is clear that the heat thrown out by 
either one of the two focal bodies radiates on all sides. But I 
shall consider only the part which strikes the mirror of which 
it is the focus. 

This heat is reflected parallel to the axis. Striking the op- 
posite mirror in this direction, it is reflected to the focus of 
this second mirror and enters as a consequence the body which 
occupies this focus. Similarly inversely, the heat thrown out 
by this latter against its mirror enters after two reflections the 
body which occupies the focus of the first mirror. 

Let us suppose, first, the two focal bodies are at the same 
temperature, or each one sending out in equal intervals of time 
an equal quantity of radiant heat to its own mirror. The 
relative equilibrium of heat between the two focal bodies will 
not be disturbed by this operation, ; for each of them will re- 
ceive from the other exactly what it gives up to it. Radiation 
will exactly compensate absorption. 

Now let us change, to a greater or less degree, the tempera- 
ture of one of the two focal bodies ; the exchanges made between 
them by means of double reflection will cease to be equal : the 
relative equilibrium will be destroyed. It will tend then to re- 
establish itself, and the temperature of these two bodies will ap- 
proach each other. If additional heat should be thrown upon 
the first body, for example, a tenth of all that which it has, the 
second body will make advantageous exchanges with it. For 
ten particles transmitted by reflection, it will receive eleven by 
the same means : in this way its heat will be augmented. 

If one should withdraw heat from the first body, for example 
a tenth, the- second body will make exchanges at a loss, receiving 
nine against ten by means of the mirror. It will be cooled. 

Such is the result of the theory conforming exactly to that 
of the ingenious experiments of M. Pictet, in spite of all the 



conditions which 1 have made, since these conditions influence 
only the quantity of cold or of heat produced by reflection, 
and not the nature of these actions. It is known that this 
physicist has observed heat and cold equally reflected in his ap- 
paratus, which is such as I have just described. He has not 
hesitated to explain the reflection of cold just as that of heat in 
a reciprocal sense : but being limited (conformably to his 
representation) to explanations drawn at once from experiment, 
and it not being his purpose, in the important work which he 
has published, to treat of the constitution of discrete fluids, he 
has not been able to enter into the details which I have just 
given. It has resulted from this that the view to which he has 
come touching the cause of the reflection of cold, founded upon 
these notions of equilibrium, inapplicable to discrete fluids, is 
insufficient for the theory, however true as to appearances. 

It is certain that when one produces cold at the focus of one 
of the mirrors, the heat of the thermometer placed at the op- 
posite focus follows the course which M. Pictet traces for it. 
And this course is what I have just described. But what it is 
that causes the excess heat of the thermometer to take this 
course, this physicist has not shown me, because he has not 
been called upon to consider heat according to its natural con- 
stitution. Now if one holds to the ideas of tension, of stress, 
in a word, of unvariable equilibrium, he finds that the progress 
of the phenomenon of heat in the experiment of the reflection 
of cold remains absolutely inexplicable. I shall now show, (1) 
that in this hypothesis of unvarying equilibrium no heat ought 
to pass from the thermometer to its mirror, (2) that if any does 
pass, this heat should not converge to the focus of the other 



(I) At the instant when one places a cold body, such as glass, 
at the focus of one of the mirrors, the heat of all the neighbor- 
ing bodies passes into it. This cause acts according to the law 
B 9 


of the inverse square of the distance, when we suppose the 
bodies to be of the same nature, as we do in this instance. 

The mirrors employed in the experiment of the reflection of 
cold were placed ten and one half feet apart. Their curvature 
was that of a sphere with a radius of nine inches : so that their 
foci were about four and one half inches from their surface, 
measured on the axis. 

If, then, we consider only the apparatus without taking into 
account the supports, or the air or the surrounding and neigh- 
boring bodies, it is clear that the mirror whose focus is occu- 
pied by the glass, being twenty-eight times nearer this cold 
body than the other mirror, ought to send out to it seven him-, 
dred and eighty-four times as much heat in the same time. 

Further, the thermometer placed at the focus of this other 
mirror being nearer the glass than its mirror in the ratio of 26 
to 27, ought to set free more heat than a portion of the mirror 
equal to its bulb in the double inverse ratio (at least for the 
part of the mirror which lies at the origin of the axis). This 
ratio is that of 729 to 676, or of about 13 to 12 ; so that, 
through the direct influence of the glass, the thermometer loses 
about a thirteenth more of its heat than if it formed a part of 
the mirror, at the focus of which it is placed. When the cool- 
ing of the first mirror becomes sensibly equal to the second, the 
thermometer being less distant than the former, is also more 
affected by the latter in the double inverse ratio of 27 to 28 ; 
that is to say, in the ratio of 784 to 729, or of about 14 to 13. 

Thus the thermometer is cooled more than its mirror, either 
directly by the glass, or indirectly by the mirror whose focus 
this glass occupies. Heat here then is under less tension than 
in the mirror. Consequently it cannot pass from the thermome- 
ter to the mirror, nor in consequence, radiate from there to the 
opposite mirror next the glass. This progress of the phenomena 
in a system in unvarying equilibrium is contrary to the effect 
which the cause should occasion. And it is still more inexpli- 
cable when we consider the supports of the apparatus and all 
the surrounding bodies which send heat into the glass, and 
constantly draw out that of the thermometer, as well as of the 
opposite mirror: effects independent of reflection and of the 
particular position of the foci. 



(II). To which it is necessary to add, in reconciling the 
same (which is demonstrated false in the hypothesis I have dis- 
cussed), that the heat of the thermometer passes in part into 
its mirror; as there is carried over only what replaces that which 
escapes, this heat would not be reflected, but absorbed. Now, 
all the heat which one of the mirrors sends out to the other, 
aside from that by reflection to the focus, being an irregular 
radiation, would not converge at the focus of the other mirror. 
THUS the foci would not be more characteristic than two other 
points, taken at random between the mirrors, for repeating the 
experiment of reflection of cold, which is absolutely contrary 
to the actual observation. 

It is apparent, then, that if we refuse to consider heat 
according to its true constitution as a discrete fluid, whose 
particles are in motion, and if in consequence we do not arrive 
at ideas which I have given of the equilibrium of radiant free 
heat, it is impossible to give any satisfactory explanation (com- 
patible moreover with the principles of sound physics), of this 
beautiful and remarkable phenomenon of the reflection of cold. 
The fact is established by an excellent observer, who has very 
clearly recognized the progress of the phenomena of heat. The 
discovery of the cause is due to the author of the true theory of 
discrete fluids. 



(1). Radiant heat is only a part of the heat that escapes from 
a hot body. Let us suppose that in the preceding experiment 
the two foci of the mirrors communicate by a metallic bar, termi- 
nated at both ends by these foci: if we place at one end of the 
extremities of this bar an exhaustless source of heat (a red-hot 
iron, a blast-lamp flame, the focus of a powerful lens): immedi- 
ately the radiant heat, following the course indicated above, 
will warm the other extremity of the bar by the double reflec- 
tion. At the same time the non-radiant heat, creeping gradu- 


ally into the contiguous parts of the bar, will slowly heat it and 
will finally come to the points most distant from the source. 

The air being a discrete fluid much more dense 1 than heat, 
arrests and intercepts the particles of the latter. But being 
much more rare than the metal, it allows a portion of it to pass, 
which produces the phenomena of radiant heat. Light, much 
more rare and subtle than heat, is transmitted in much greater 
proportion by this same air, the opacity of which is so incon- 
siderable that it becomes sensible only in very great masses. 2 
The transparency or the quantity of fluid transmitted through 
another fluid, depends upon the rarity and the subtlety of the 
particles of both fluids. I do not speak here of the affinities 
and capacities of different bodies for heat. I speak only of the 
mechanical interception of this fluid by its solid parts. This 
interception is sufficient only to produce these two kinds of 
heat or of cold, radiant heat, and nonradiant heat. 

Entangled, further, in the small cavities or in the interstices 
of solid particles, the heat may or may not recover all the veloc- 
ity which properly belongs to it, according as these cavities or 
interstices are or are not sufficiently spacious. When it recov- 
ers only a portion of its velocity, it becomes in part insensible 
or latent. When it can recover only a very little of it or none 
at all, it yields to the affinities of the particles which surround 
it and combines in a thousand ways. 

(2). Heat is not the only fluid of its kind. Several discrete 
fluids are known, radiant and nonradiant. 3 We often have 
occasion to consider these fluids in the state of equilibrium. 
The determination of the true sense of this word ought then to 
be of much importance, independently of the theory of heat. 

1 The density which I attribute to the air in this instance, consists 
chiefly in the proximity of its molecules; for a discrete fluid maybe 
composed of very dense particles, but with large spaces between them : 
so that it could be more permeable than heat, although more dense. 

2 Notice the remarks of M. de Saussure, upon the transparency of 
the air, in his memoirs upon light. Academ. de Turin, 1790. 

8 In the electrical phenomena, there are radiations of the correspond- 
ing fluid. In magnetic phenomena neither of the two magnetic fluids is 



If these remarks and the preceding discussion offer any 
useful views, if they tend to throw light upon an important 
class of phenomena, if they suggest any clear ideas upon the 
method of motion of invisible and subtle fluids which manifest 
their existence by such diverse appearances : finally, if these 
conceptions naturally connect themselves with other theories, 
either already proven, or rendered probable, concerning the 
various effects of these subtle fluids (such, as the phenomena of 
evaporation, of electricity and of magnetism), is it not the 
requital of investigating the general theory upon which all 
these special explanations depend ? This theory (I refer to 
that of M. le Sage of Geneva, upon the nature of discrete 
fluids) merits the further attention of physicists, since it depends, 
itself, upon another principle, more general, which has also as 
a proof of its reliability, the clear and satisfactory explanation 
of very striking and very general phenomena, absolutely in- 
explicable without it. 





Geneva, 1809. 




Questions Relative to the Nature of Caloric . _ . . 17 
Resume of Principles and Conclusions. . . . . 19 



CHAPTER IV. PP. 6 10. 

THE word caloric (heat) has been originated to explain the 
cause of heat, with the formally expressed intention of being 
non-committal as to its nature. 

It is desirable to leave it indefinite as to whether heat may be 
produced by a specific fluid, or, merely, be a movement 
impressed upon the molecules of a body, without the introduc- 
tion of any fluid. 

Many noted physicists believe there is no specific fluid to 
which this word caloric is applicable. They believe that heat 
is produced by internal movements of the molecules of a body. 
More often, however, physicists have recourse to a vibrating 
ether or to the air, or to some other medium propagating waves 
to which they attribute the phenomena of heat. 

Others believe that caloric is a specific fluid, which penetrates 
the body and produces all the appearances of this kind. 

Among the latter, many believe that caloric and light are 
identical. Others are of a contrary opinion. 

Some look upon caloric as simple ; a smaller number regard it 
as a compound fluid. Mr. J. A. DeLuc believes that caloricis, a 
kind of vapor composed of ponderable matter held in a state of 
suspension by light. This conception throws some light upon 
many phenomena and merits serious consideration. Meanwhile, 
pressed to arrive at the chief object which I have in view, I 
will refrain from all discussion as to the composition of caloric. 

I have no desire to repeat here and weigh the general 
arguments stated on the one side and on the other for sus- 
taining the various views which I have just outlined. I will 
limit myself to a very few remarks on this subject. 

As stated below I propose to consider caloric as a specific 
fluid. I will represent the radiations of this fluid as an emission 



and never as an undulation. I believe this conception and this 
representation to be more conformable than any other to the 
nature of things and founded upon the soundest principles of 
general physics. But if those who believe otherwise substitute 
waves for an emission they may be able, perhaps, to adapt to 
their opinion the explanations which I give for phenomena of 
this crass. It is no desire of mine that they should attempt it, 
because I am persuaded that this would be translating a 
language clear and natural into a language obscure and artificial. 
But I make this statement to make clear the kind of work 
which I have undertaken. I do not contest any system. I do 
not refute any explanation. It is my aim, in limiting myself in 
my subject, to explain in my own way what seems to me to ad- 
mit of clear explanation, and to indicate the phenomena of 
which the explanation remains imperfect. If each one who 
has an opinion upon the theory of caloric will give a concise ex- 
position of his ideas on the subject, and will show how the facts 
may be coordinated by means of these conceptions : physicists 
can see at a glance which theory is most satisfactory, or if all 
should be rejected. 


SECTION IX. pp. 258261. 

HEAT is a discrete fluid; each element of heat follows con- 
stantly the same straight line, as long as no obstacle arrests it. 
Every point of a hot space is constantly traversed throughout 
by streams of heat. 

If we admit this constitution of heat, the following conclu- 
sions are inevitable. 

The first three require nothing further. The others require 
the assumption that heat is comparable with light in its move- 
ments of reflection and refraction. 

1st. conclusion: Free heat is a radiant fluid. Or, as the 
surface of the body of heat becomes free, each point of the sur- 



face of the body is a center to which tend, and from which are 
carried, in every direction, streams of heat. 

2nd. conclusion : The equilibrium of heat between two 
neighboring free spaces consists in the equality of the 

3rd. conclusion: When the equilibrium is disturbed, it is 
reestablished by unequal exchanges, in a medium of constant 
temperature, a body that is hotter or colder requires this tem- 
perature according to the law that the periods of time being in 
arithmetical progression, the differences of temperature are in 
geometrical progression. 

4th. conclusion: In a space of uniform temperatures, if a 
reflecting or refracting surface is introduced it has no effect in 
changing the temperature of any part of this space. 

5th. conclusion: In a space of unequal temperature, if there 
is placed a body which is either hotter or colder and if after- 
wards a reflecting or refracting surface be introduced, the 
points, upon which these surfaces direct the rays emanating 
from this body, will be affected by it, being heated if the 
body is hotter, or cooled if it is colder. 

6th. conclusion: A reflecting body, having been heated or 
cooled internally, recovers the surrounding temperature more 
slowly than a nonreflector. 

7th. conclusion: A reflecting body, having been heated or 
cooled internally will have less effect on another body placed 
at any distance (in heating or cooling it) than a nonreflector 
would under the same conditions. 

All these conclusions have been verified experimentally, ex- 
cept that concerning the refraction of cold. This experiment 
remains to be made, and I am confident of the result, at least 
if the refraction of the heat is capable of being observed. This 
result is indicated in the 4th. and 5th. conclusions, which could 
in this way be submitted to a new test. It is hardly necessary 
to indicate in this place the precautions by means of which one 
would place himself beyond every kind of misobservation. 




PIERRE PREVOST was born in Geneva, March 3, 1751, and died 
at the same place oil the 9th of April, 1839. He was the son of 
a clergyman and was educated for a clerical career, but turned 
his attention to law and later to educational work. He became 
a professor of philosophy and a member of the Academy of 
Sciences at Berlin in 1780. Here, through his acquaintance 
with Lagrange, his attention was directed to science, which 
later he followed up with his studies on Magnetism and Heat 
at Geneva where he became professor of physics in 1810. He 
published much on different subjects, including philology, 
philosophy, political economy, fine arts, etc. He issued the 
works of le Sage, supplemented by many additions of his 
own. His Du Calorique Rayonnant appeared at Geneva in 
1809 and was an exposition and extension of his theory of ex- 
changes first advanced several years before. The original 
memoir and later publications appeared in the Journal de 
Physique and the Phil. Trans, from 1791 to 1802. His remark- 
able versatility is indicated in the variety of his publications. 
His most valuable contribution to science is undoubtedly his 
Theory of Exchanges one of the most important principles in 
the whole range of physical science. 








Transactions of the Royal Society of Edinburgh. 
Vol. XXII. Part I. pp. 120. March, 1858. 



Division of Subject 23 

Description of Instruments and Method . . . .24 

On Radiations from plates of Different Substances . . 26 
On Radiations from Polished Surf aces . . .32 

On Radiations of Plates of Different thicknesses . . 33 

Results Explained by Prevost's Ttieory of Exchanges . . 35 
Peculiarities of the Radiation from Plates of Diatherm- 

anous Substances 37 

Equality of the Radiation and the Absorption . 40 
Influence of the Reflective and Refractive Powers of Bod- 
ies on their Radiation considered 42 

Equal and Independent Radiation ..... 47 

Internal Radiation and Conduction , 49 





Read, 15th, March 1858. 

Division of Subject. 

1. This paper consists of two parts, the first of which is 
confined to describing the experiments performed; while in 
the second it is attempted to connect these with certain theo- 
retical views regarding Radiant Heat. 

2. The experiments were made with a fourfold object; at 
least for the sake of clearness, it is well to class them into four 
distinct groups: 

Group L Contains those experiments in which the quanti- 
ties of heat radiated from polished plates of different 
substances, at a given temperature, are compared with 
the quantity radiated from a similar surface of lamp- 
black, at the same temperature. 

Group II. Those in which the quantities of heat radiated 
at the same temperature, from polished plates of the same 
substance, but of different thicknesses, are compared 
with one another. 

Group III. Those in which the radiations, from polished 
plates of different substances at any temperature, are 
compared with that from lampblack at the same tem- 
perature, with regard to the quality or nature of the 
heat radiated. 



Group IV. Those in which the same comparison is made 
between the radiations from polished plates of the same 
substance, but of different thicknesses. 

Instruments used, and Method of using them. 

3. I am indebted to the kindness of Professor Forbes for 
the use of a delicate thermo-multiplier, consisting of the sen- 
tient pile, and its attached galvanometer and telescope; as 
well as for much valuable information with regard to the 
proper method of using the apparatus. 

The following arrangement was adopted for the great mass 
of the experiments: 

A. Is the sentient pile, with a polished brass cone attache^ 
to it, for collecting the rays of heat. 

B. Is the galvanometer, the position of its needle being 
read to ^th of a degree by the telescope C. 

D. Is a screen placed before the mouth of the cone in 
which there is a small hole or diaphragm .65 inch square. The 
screen is covered with gilt paper, in order that, should it get 
slightly heated, it might radiate as little as possible. 

The heated body is placed behind the diaphragm, filling up 
the field of view from the cone ; so that every ray reaching the 
cone from behind the diaphragm comes from the heated body. 



In the following experiments, unless the contrary is men- 
tioned, the distance of the diaphragm from the mouth of the 
cone is 2 inches. 

The dimensions of the cone itself are as follows : 

Length of axis, or distance between centre of mouth and 

pile, 5 inches. 

Diameter of mouth or opening, 2.6 inches. 

The temperature to which the heated body was raised was 
generally 212, and the apparatus used for heating it was of the 
following construction : 

It consisted of a tin vessel, having its top, bottom, and sides 
double (or a box within a box), and furnished on the top with 
a lid, also double, by means of which the body to be heated was 
introduced into the interior. 
Water was poured into the 
chamber between the outer and 
inner boxes, and allowed to 
boil ; and, when the lid was 
shut, the temperature of the 
interior was found to rise very 
nearly to the boiling point ; a 
thermometer placed in the 
air of the chamber showing a 

temperature of 200, and when lying on the bottom, 
a temperature of 210. When an observation was to be made, 
the hot body was taken out, and that surface which lay on the 
bottom of the inner chamber placed behind the diaphragm, so 
as to radiate into the cone. In the following experiments, un- 
less the contrary is mentioned, the body has been heated in this 

The first swing of the galvanometer needle was taken as rep- 
resenting the intensity of the heating effect : and Professor 
Forbes has shown, in a paper read before this Society, 2d May, 
1836, that this will hold up to angles of about 20, which is the 
maximum deviation used in these experiments. 

Observations were always made with as little sunlight as pos- 
sible ; and under these circumstances, it was ascertained that 
the stray heat reaching the cone was inappreciable. The needle, 
it was calculated, reached the limit of its swing about 12 



seconds after the heated body had been taken out of the 
boiling-water apparatus. 

Experiments were made to ascertain if the body cooled 
sensibly during this short period of time, and it was found that 
its cooling was so trifling as not to interfere in any degree with 
the results of these observations. In the following experiments, 
it is therefore assumed that the body remains at its original 
temperature of 210 while the observation is being made. 

Four observations were generally made, and three if they 
agreed together exceedingly well, but never fewer. Very often 
the agreement was exact. . 

First Grout of Experiments described. 

4. With these remarks, I proceed to describe the experiments 
belonging to the first group, or those made with the view of 
comparing the heat radiated from polished plates of different 
substances with that radiated from a surface of lampblack at 
the same temperature. 

The reason why lampblack was chosen as the standard is ob- 
vious ; for, it is known from Leslie's observations, that the 
radiating power -of a surface is proportional to its absorbing 
power. Lampblack, which absorbs all the rays that fall upon 
it, and therefore possesses the greatest possible absorbing power, 
will possess also the greatest possible radiating power. The first 
substance compared with it was glass. 

A. Glass. Apiece of plate glass, .3 inch thick, having paper 
coated with lampblack pasted on its surface next the pile, gave 
a deviation of 18.1. This may be taken as the radiation from 

Three plates of crown glass, each .05 inch thick, placed 

one behind the other, gave 17.7. 

A single piece of crown glass of the same thickness, 
gave 16.5. 

This difference is probably owing to the single plate cooling 
faster than the three plates. It may be argued that the 
radiation from the glass is very nearly equal to that from lamp- 
black ; and indeed this is already well known.* 

* See Leslie's " Inquiry into Nature and Propagation of Heat." 



B. Alum. Here the boiling- water apparatus could not be 
used, since alum becomes calcined at a temperature much 
below 212 ; but a self-regulating apparatus, invented by the 
late Mr. Kemp, was employed instead, giving a steady 
temperature of 98. 

A piece of plate glass .18 inch in thickness, gave 5.0 

A piece of alum of the same thickness gave 5.0 

The radiation from the alum may therefore be reckoned 
equal to that from glass. 

C. Selenite. At the temperature of 98 

A piece of selenite .125 inch in thickness gave. . . .5.1 

Under the same circumstances, glass .18 inch thick 

gave 5.0 

In the boiling-water apparatus, 

The same piece of selenite gave 18.0 

While blackened glass gave 18.5 

The radiation from selenite may therefore be reckoned equal 
to that of alum or glass. 

D. Mica. A small box was constructed, having two windows 
of mica, the thickness of the mica in the one being .0009 inch, 
and of that in the other. 02 inch. This box was filled with 
mercury (Professor Forbes having suggested the use of that 
metal, to keep up the temperature, while interfering very little 
with the radiation). The whole was then set on a glass dish in 
the boil ing- water apparatus. 

The radiation from the thin window was 11.2 

While that from the thick window was 12.7 

As it would have been manifestly erroneous to compare these 
with the radiation from the blackened glass lying in contact 
with the bottom of the apparatus, the thin window was 
removed, and the blackened paper substituted in place of it. 

While the thick mica window gave 12.7 

The blackened paper gave 13.8 

In comparing the radiations from the two windows, they 
were observed alternately. We see, therefore, that the radia- 
tion from mica, especially thin mica, is less than from lamp- 



black in the proportion of 11.2 to 13.8, or the heat from thin 
mica is 80 per cent of that from lampblack. 

E. Rock Salt. As in the experiments with rock salt, it was 
desirable to obtain results of the greatest possible accuracy, the 
radiation from rock salt was not compared with that from 
blackened glass ; for it was found that glass cooled more 
rapidly than rock salt. 

The following plan was adopted : 

A piece of rock salt .18 inch thick (the temperature as 
in all the previous examples being about 210, gave 3.2 
A canister with water kept boiling, coated with lamp- 
black 22.0 

In order to estimate how much the rock salt had cooled 
during the observation, the following experiment was made, 
without any diaphragm : 

Rock salt .18 inch thick taken to the cone at once, 

gave 5.1 

After cooling for 15 seconds, it gave 4.9 

It will be seen from this, that were the rock salt, instead of 
cooling during the 12 seconds necessary for the observation, 
kept at the temperature of 212 , it would not have given more 
than 3.3, while the hot-water canister gave 22.0. 

5. From these experiments, it appears that glass, alum, and 
selenite, at low temperatures, have an intensity of radiation 
very nearly equal to that from lampblack ; while mica radiates 
somewhat less, and rock salt greatly less. This is shown by 
the following table : 






Lampblack, > 









Thick mica, 

Thin mica, 

Rock salt 



Second Group of Experiments described. 

6. I now proceed to the second group of experiments, or those 
designed to compare together the quantities of heat radiated 
at the same temperature from polished plates of the same sub- 
stance, but of different thicknesses. 

A. Glass. No direct experiment of this kind was made on 
glass ; for although a thick plate gave a somewhat greater 
radiation than a thin plate, it was imagined that this was due 
to the unequal cooling of the two plates. Indirectly, however, 
we may gather that thick glass radiates somewhat more than 
thin glass, from the following experiment, which belongs more 
properly to the fourth group: 

A plate of crown glass .05 inch thick, being placed be- 
fore the cone as a screen, and a similar plate .05 inch 
thick, and 3.75 inches square, being used as the 
source of heat at a distance of 6 inches, and no dia- 
phragm used, the deviation was 0.95* 

But when the source of heat was a similar plate .10 
inch thick, the deviation became 1.45 

Such a difference cannot be accounted for by the unequal 
cooling of the plates ; and it would seem to indicate that a small 
quantity of heat from the interior of the thick plate reached 
the surface ; which heat, having already been sifted by. its pas- 
sage through glass, was easily able to pierce the screen. 

In another similar experiment, 

One piece of crown glass .05 inch thick, gave a deviation 

of 1.1 

Two plates .05 inch thick, the one behind the other, 1.55 
Three such plates, 1.9 

B. and C. No experiments of this kind were attempted with 
alum or selenite. 

D. Mica. Experiments similar to those already described, 
only at a distance of 2^ inches from the cone, gave 

* Without any screen, it was calculated that the intensity of effect 
would have been equal to about 150. 


For mica .0009 inch thick (average of two sets of experi- 
men ts), 8.2 

For mica, .02 inch thick (average of two sets of experi- 
ments), .9.3 

The experiments already quoted, which were made at a 
shorter distance from the pile, gave 

For mica, .0009 inch thick, 11.2 

For mica, .02 inch thick, 12.7 

E. Rock Salt. Three pieces of rock salt were used. Their 
dimensions were: 

1st Piece. 2nd Piece. 3rd Piece. 

Length 1.15 inch 2.15 inches 2.5 inches 

Breadth 1.15 " 1.4 inch 1.4 inch 

Thickness... .0.18 " 0.36 " 0.77 " 

For these pieces, as well as for the other substances, I am in- 
debted to the kindness of Professor Forbes. When placed be- 
hind the diaphragm, the farthest off surface was large enough 
to fill up the field of view, that is to say, all rays from the 
cone striking the nearest surface struck also the surface far- 
thest off ; the distance between the two surfaces being the 
thickness of the piece. 

The following are the means of four sets of experiments : 

Radiation from 1st or thinnest piece 3.4 

" ' 2nd or middle piece 4.3 

" (( 3rd or thickest piece 5.3 

This proves that more heat is radiated by a thick than by a 
thin piece of rock salt. 

The following experiments were devised by Professor Forbes, 
to confirm the above results. 

(a.) The second piece of rock salt was placed obliquely behind 
the diaphragm, making an angle of 20 with the prolongation 
of the axis of the cone. A piece of fir wood of the same dimen- 
sions was placed in the same way. The two substances being 
compared in this position, and also in the usual position behind 



diaphragm (viz., perpendicular to the direction of the cone's 

axis), the following was the result : 

Oblique. Usual position. 

Rock salt .36 inch thick, 4.0 4.0 

Wood, same size as rock salt, 9.1 14.1 

In order that this experiment may be understood, it may be 
well to mention, that, when the plate was placed obliquely be- 
hind the diaphragm it did not quite fill up the field of view. 
Hence the wood gave out less heat to the cone in this than in 
its ordinary position. 

It appears, therefore, that the radiation from rock salt, in a 
direction making a small angle with the surface, bears a 
greater proportion to the corresponding radiation from wood 
than when both radiations are taken perpendicular to the sur- 
face. The reason undoubtedly is, that in the former case the 
rays come from a greater thickness of the substance, so that 
their intensity is increased. 

P. The middle-sized piece of rock salt was bound tightly 
to the thickest piece, with a slip of tin foil between, so that 
the whole might cool as one piece, and thus obviate any ob- 
jection that might be brought against the results, founded on 
the unequal cooling of the plates, owing to their thicknesses 
being different. 

The surface of the middle-sized piece facing the pile, 

gave 6.3 

That of the thickest piece, gave 8.1 

The plates, therefore, still retain their inequality of radia- 
tion; but the amount from each was increased, owing, no doubt, 
to the reflection and radiation from the tin foil. The radiation 
from the tin foil may be estimated at 1.0, deducting which, 
we have 5.3 and 7.1; the increase now being due to reflection 
from the tin foil. 

7, It thus appears, that while the difference between the 
radiating power of thick and thin glass is so small as not to be 
capable of being directly observed, there is a perceptible differ- 
ence between the radiation from thick and thin mica, and a 



still more marked difference between the radiation from plates 
of rock salt of unequal thickness. 

But (at least with the thicknesses used) the greatest radia- 
tions from mica and rock salt were still below that from lamp- 
black, and the radiation from rock salt greatly so. 

The following table exhibits the results of the second group 
of experiments: 










Rock salt, 


Middle 81 
thin ) C4 

Third Group of Experiments described. 

8. I now proceed to consider the third group of experi- 
ments, or those made with the view of comparing the radiations 
from various polished surfaces with that from lampblack, as 
regards the quality of the heat; its quality being tested by its 
capability of transmission through a screen of the same mate- 
rial as the radiating plate. 

A. Glass. In an experiment already described, where a 
plate of crown glass .05 inch thick was used as a screen, and 
a similar plate of crown glass as a source of heat 

We had , 0.95 

A similar plate .1 inch thick as the source of heat, 
gave 1.45 

Blackened paper attached to a similar surface of plate 
glass, .3 inch thick, the blackened side being next 
the pile, , 1.95 

Therefore heat from a thin plate of glass is less transmissible 
through glass than heat from blackened paper. 

B. and C. No experiment of this nature was made with 
alum or selenite. 

D. Mica. The apparatus already described gave 



Without With mica screen 
screen. .0025 inch thick. 

For window (the window, it will 
be borne in mind, is the radia- 
ting surface), .0009 inch thick. .11.2 2.5 

Window .02 inch thick 12.7 3.2 

Blackened paper attached to 
glass lying on the bottom of 
the boiling-water appara- 
tus, gave 21.0 6.3 

We have therefore the proportion of heat passed by mica 

For heat from thin mica window, 223 

" " thick " " 260 

" " blackened paper, 300 

E. Rock salt. The thickest piece of rock salt (thickness 
.77 inch) being used as a screen, and the diaphragm withdrawn, 
in order to give greater results; the middle sized piece of rock 
salt gave 

With screen. Without screen 
6.1 19,6 

The same screen stopped 3 rays out of 12 for ordinary lamp- 
black heat. 

This experiment is sufficient to show that rock salt is much 
less diathermanous for heat from rock salt than for ordinary 
heat. The common opinion, that rock salt is equally diather- 
manous for all descriptions of heat, is therefore untenable. 

9. From the third group of experiments it appears, therefore, 
that heat emitted by glass, mica, or rock salt, is less trans- 
missible through a screen of the same material as the heated 
plate, than heat from lampblack ; this difference being very 
marked in the case of rock salt. 

Fourth Group of Experiments described. 

10. 1 now proceed to the fourth group of experiments, or 
those made with the view of comparing the radiations of plates 
of the same substance, but of different thicknesses, with regard 
to the quality of the heat radiated. 



A. Glass. It has been already shown (Art. 8), that heat 
from crown glass .05 inch thick is less transmissible through 
glass, than that from crown glass .10 inch thick. 

B. and 0. No experiments of the kind were made on alum 
or selenite. 

D. Mica. It has been already shown (Art. 8), that heat from 
thin mica is less transmissible through a mica screen than heat 
from thick mica. 

E. Rock salt. With a screen of rock salt .18 inch thick, the 
following result was obtained : 

Thickest piece of rock salt, heated to 210 

(thickness .77 inch), gave 2.5 

Middle-sized piece of rock salt, heated to 210 

(thickness .36 inch), gave 1.7 

Thinnest piece of rock salt, heated to 210 

(thickness .18 inch), gave 1.1 

Without any screen, the same pieces gave 

Thickest, 4.9 

Middle-sized, 4.1 

Thinnest, 3.3 

Proportion of heat from thickest piece passed 51 

Proportion of heat from middle-sized piece passed .41 

Proportion of heat from thinnest piece passed 33 

A similar experiment, with a screen .29 inch thick gave 

With screen. Without screen. Proportion passed. 

Thickest piece. . .2.6 5.4 .48 

Middle-sized, ....1.8 4.5 .40 

Thinnest 1.2 3.5 .33 

It follows from this, that a screen of rock salt passes heat 
from thick, more easily than heat from thin rock salt, 

11. From this fourth group of experiments, we learn that heat 
from thick plates of glass, mica, or rock salt, is more easily 
transmitted by screens of the same nature as the heated plate 
than heat from thin plates of these materials. 

The following table exhibits the results of the third and 
fourth group of experiments : 



No. of Rays out of every 
100 that pass through 
a screen of the same 

No. of Rays of 
Heat out of 


material as the source 
of Heat in 1st column, 

every 100 

the screen being of 
only one thickness for 

that pass 
through the 

each material. 

same screen 

Glass (crown ^th inch thick), 



Glass (crown ^th inch thick), 

1.0 } 

Mica (thickness .0009 inch), 


Mica (thickness .02 inch), 



Rock salt (thickness .18 inch), 


(Art. 12) 

Rock salt (thickness .36 inch), 

41 [ 


Rock salt (thickness .77 inch), 



Results deducible from the foregoing Experiments. 

12. These experiments, as well as others yet to be described, 
may be explained by Prevost's theory of exchanges, somewhat 

In the first place, it would seem to be a consequence of this 
theory, that radiation must take place from the interior as well 
as from the surfaces of bodies. For, suppose that we have two 

indefinitely extended surfaces of 
lampblack, as in the figure, and 
between them a plate of rock 
salt of a certain thickness, also 
indefinitely extended; and let 
the whole be kept at the same 
temperature. Then, since the 
temperature of the. rock salt 
remains the same, it must radiate 
as much as it absorbs. But a thicker plate of rock salt, placed 
under the same circumstances, would absorb more of the heat 
radiated from the lampblack because each ray would have to 
pass through a greater depth of the substance of salt; hence a 
thick plate of rock salt must radiate more than a thin plate. 
We see likewise, the reason for the small radiative capacity of 



rock salt to be its small absorptive capacity. In order to prove 
this deduction from Prevost's theory experimentally true, the 
following experiment was devised: 

A boiling-water canister, coated with lampblack, was put 
behind the diaphragm, filling up the field of view, and the 
three pieces of rock salt heretofore used as sources of heat, 
were now separately used as screens, being put before the dia- 
phragm, so that the heat from the canister had to pass 
through their substance before reaching the cone. The follow- 
ing was the result: 

Without any Screen of Screen of Screen of 

screen. Rock salt Rock salt Rock salt 

.18 inch .36 inch .77 inch 

thick. thick. thick. 

Eadiation from canister, 21.3 17.6 16.8 15.8 

The difference between heat absorbed by plate, 
thickness = .18 inch, and that absorbed by 
plate, thickness = .36 inch, 

is 1.2) 

Another similar experiment gives 0.9 J Mean *! 

The difference between heat absorbed by plate, 
thickness = .36 inch and that absorbed by 
plate, thickness = .77 inch, 

is 1.0 ) 

Another similar experiment gives 1.3 f Mean 1.1 

These should nearly correspond to the differences between the 
radiation from the same place, under their ordinary circum- 
stances of position (if the theory be true which asserts that the 
absorption of such a plate equals its radiation); accordingly we 
find that 

The difference between heat radiated by 

plate, thickness = .18 inch ) -.- 

And that radiated by plate thickness = .36 inch, ) 
While the difference between radiation of 

plate thickness = .36 inch } 

And that of plate thickness = .77 inch, f Is 1<0 

(Art. 6, mean of four sets of experiments.) 
We see, therefore, that there is an agreement between the 
two sets of differences, as near as can be reasonably expected. 



13. If we now suppose a plate of glass, arid not a plate of 
rock salt, placed between surfaces of lampblack, the plate, 
whether thin or thick, will allow scarcely any heat to pass 
through it; and, consequently, plates of different thicknesses 
will all absorb very nearly the same amount, that is, nearly 
all that enters them. In this case, therefore, the radiation 
(which is equal to the absorption) will be very slightly increased 
by an increase of thickness of the plate. Also the amount of 
heat radiated, being equal to the heat absorbed, will be very 
nearly as great as that from lampblack. 

14. There are, therefore, two peculiarities of the radiation 
from plates of diathermanous substances, and which are most 
marked for those substances which are most diathermanons. 

1st, That the amount of radiation from such plates is less 
than that from lampblack. 

2d, That the amount of radiation from such plates increases 
with the thickness of the plate. 

The correlation between these different properties of bodies 
is seen from the following table: 


Bodies ranked according 
to their Radiating Ca 
pacity (least radiating 

Bodies ranked ac- 
cording to their 
(most diatherman- 

Bodies ranked according 
to the proportion by 
which their Radiation 
is increased by increas- 


ous first). 

ing the thickness. 

A stratum of heated gas 

(from Melloni's Exper- 


A stratum of gas. 

Rock salt. 

Rock salt. 

Rock salt. 




Glass. j 

Glass. ^ 


Selenite. > 

Selenite. ? 


Alum. ) 


15. The reason why radiation has hitherto been supposed to 
be -confined to the surface, or to an exceedingly small distance 
below the surface of a body now becomes obvious. The effect of 
coating a surface of polished metal with gum, for instance, is 



to increase the radiation; but, after a very small thickness of 
film, an additional coating is powerless to increase the radiation; 
the reason being, not that radiation is incapable, in all cases, of 
taking place except at the surface; but because such films be- 
ing exceedingly impervious to heat of low temperatures, the 
radiation from them is very little increased by increasing their 

Since, therefore, it appears that radiation takes place from 
the interior as well as from the surface of bodies, the question 
arises, are we to suppose each particle of each substance to 
have, at a given temperature an independent radiation of its 
own, equal, of course, in all directions ? A priori, this is the 
most probable supposition, and it seems likewise to be conform- 
able to experiment. 

16. In an experiment already described, 

A plate of crown glass .05 inch in thickness being used as 
a screen, the quantity of heat radiated from crown 
glass .05 inch thick that passed, was 0.95 

While of that radiated from crown glass, .10 inch thick 
there passed 1.45 

Another experiment gave 

Quantity of heat from crown glass .05 there passed . .1.1 

Quantity radiated from two plates of crown glass, each 
.05 inch thick the one placed loosely behind the 
other, 1.55 

From this we may infer, that the radiation from two plates 
of glass placed loosely behind each other is the same as the ra- 
diation from a plate of double the thickness, and, consequently, 
that the radiation from a particle of a substance does not di- 
minish owing to its being placed in the interior.* 

17. Let us now refer to the radiation from rock salt: 

The radiation from a piece .18 inch thick, was 3.4 

That from a piece .36 inch thick, was 4.3 

That from a piece .77 inch thick, was 5.3 

* The idea of this experiment was derived from a remark of Professor 
Forbes, who suggested that several plates of rock salt, the one behind 
the other, might be advantageously substituted for a thick plate of the 
same material as giving the very same result. 



Now if we suppose the radiation of a particle in the interior 
to be as intense as that of a particle at the surface, why, it may 
be asked (since rock salt is extremely diathermanous), does not 
a piece of double thickness give nearly a double radiation and 
so on, the radiation increasing very nearly as the thickness ? 

If we still hold the doctrine of an equal and independent ra- 
diation from every particle, we are shut up to the conclusion 
that rock salt must be comparatively opaque to heat radiated 
by itself, a result which is abundantly confirmed by experiment. 

Thus while the radiation from rock salt .18 inch thick, with- 
out any screen, is 3.4, with a screen of rock salt .18 inch thick 
it becomes 1.1. 

If, therefore, we have a piece of rock salt of double the 
thickness, or .36 inch thick, we should expect that the radia- 
tion from it would be = 3.4 + 1.1 = 4. 5. It is, in fact, 4.3. The 
difference (0.2) being within the limit of error of observation. 

In rock salt, therefore, we may suppose each particle to have 
an independent radiation of its own, unaffected by its distance 
from the surface. 

18. We see, therefore, that the opacity of rock salt with re- 
gard to heat radiated by itself, is a consequent of the admis- 
sion, that the radiation from rock salt does not increase so 
rapidly as the thickness increases ; ar.d this again results from 
the fact, that the absorption of heat by a plate of rock salt 
does not increase so rapidly as the thickness increases. This, 
again, is due to the fact, that the first part of the plate of rock 
salt sifts the heat so that it is more easily transmitted by the 
second part; and this confirms the result arrived at by Professor 
Forbes, who, finding that rock salt stopped heat of lower tem- 
perature rather more readily than heat of high temperature, 
concluded that there are a few rays for which rock salt is 

* To take a numerical example, let us suppose the heat from a single 
plate of rock salt to be = 1, then the heat from a plate four times the 
thickness, or (which is the same thing) the heat from four single plates, 
one behind another, should be nearly four times as much or = 4 (if we 
suppose the heat from each of these four plates to be readily passed by 
the plates between it and the pile), but the heat from the four-fold 
plates, instead of being four times as much, is not double of the heat 



We conclude, therefore, that every body which sifts heat in 
its passage through its substance is more opaque with regard 
to heat radiated by a thin slice of its own substance, than it is 
with regard to ordinary heat. 

19. This conclusion may be also stated thus: We have before 
proved (Art. 12) that the radiation of a thin slice of any sub- 
stance equals its absorption; we now add that the heat radiated 
is the same as that absorbed, with regard to quality as well 
as quantity. 

For this expresses the fact, that substances which sift heat 
are likewise opaque with respect to heat radiated by themselves. 
For, since the heat which they absorb is manifestly that kind 
of heat for which they are opaque, if the description of heat 
radiated is the same as that absorbed, then they also will be 
opaque with respect to heat radiated by themselves. Consid- 
ering, therefore, the heat of any temperature to consist of 
heterogeneous rays, we may state the law thus : " The absorp- 
tion of a plate equals its radiation, and that for every descrip- 
tion of heat. " 

20. A more rigid demonstration may be given thus: Let 
AB, and EC be two contiguous, equal, and similar plates in the 
interior of a substance of indefinite extent, kept nt a uniform 
temperature. The accumulated radiation from D 

the interior impinges on the upper surface of 

the upper plate; let us take that portion of it - A! , 

which falls on the particle A, in the direction B| 

DA. This ray, in passing from A to B, will have | 

been partly absorbed by the substance between 
A and B, but the radiation of the upper plate being equal to its 
absorption (since its temperature remains the same), the ray will 
have been just as much recruited by the united radiation of the 

from the single plate ; hence, the heat from any of the interior plates of 
the compound plate is passed with great loss, by the plates between it 
and the pile. Now, since the absorption of a plate equals its radiation, 
the reason why the four-fold plate scarcely radiates twice so much as 
the single one is, that it scarcely absorbs twice as much; and this again 
is due to the fact, that the heat after it has passed the first plate of the 
four-fold plate has become sifted, and passes with little diminution of 
intensity through the other three plates. 



particles between A and B, as it was diminished in intensity by 
their absorption. It will therefore reach B with the same 
intensity it had at A. But the quality of the ray at B will also 
be the same as its quality at A. For, if it were different, then 
either a greater or less proportion would be absorbed in its pas- 
sage from B to C, than was absorbed of the equally intense ray 
at A, in its passage between A and B. The amount of heat ab- 
sorbed by the particles between B and would therefore be 
different from that absorbed by the particles between A and B. 
But this can not be; for, on the hypothesis of an equal and in- 
dependent radiation of each particle, the radiation of the parti- 
cles between B and C is equal to that of the particles between A 
and B, and their absorption equals their radiation. Hence the 
radiation impinging on B, in the direction of DB, must be 
equal in quality as well as in quantity to that impinging upon 
A; and, consequently, the radiation of the particles between 
A and B must be equal to their absorption, as regards quality 
as well as quantity; that is, this equality between the radiation 
and absorption must hold for every individual description of 

21. The following experiment illustrates this law: 

The quantity of heat radiated from crown glass screen, 
.05 inch thick, which passes through a crown glass 
screen .05 inch thick, . . . . , = 0.95 

While that from plate glass .3 inch thick, covered with 
blackened paper (the blackened paper being next the 
pile), which passes through the same screen. .. = 1.95 

But if the surface of crown glass .05 inch thick, farthest 
from the pile, be coated with paper, the polished sur- 
face being next the pile, then the amount which passes 
the screen, = 1.85 

And if three plates, the one behind the other, of crown 
glass, each .05 inch thick, be used as the source of 
heat, the surface farthest from the pile of the farthest 
off plate only being covered with paper, the amount 
of radiation which passes the screen, = 1.95 

Such a plate of glass or series of plates, therefore, by having 
the farthest off surface coated with paper, gives out heat 



similar to that from paper or lampblack; the reason being, 
that the heat from the paper on the farthest off surface is as 
much recruited as it is absorbed by its passage through the 
glass, both as regards quantity and quality; so that the radia- 
tion which falls upon the cone is virtually that from paper or 

23. There is little difficulty in explaining why heat from a 
thick plate of any substance should pass more readily through 
a screen of the same substance than that from a thin plate. 
The reason is, that the heat from the interior of the thick 
substance, having been sifted in its passage, is, therefore, now 
more easily able to pass through a screen of the same substance. 

23. We see also why, generally speaking, bodies at the same 
temperature radiate the same quality of heat; let us, for in- 
stance, take a tolerably thick plate of glass, and a surface of 
lampblack, and compare them together. Since the plate of 
glass absorbs nearly all the rays that fall upon it, it will radiate 
nearly as much as lampblack; and since the quality of the 
radiated is the same as the quality of the absorbed heat, its 
radiated heat will very nearly have the same quality as that 
which is radiated by lampblack. 

Tlie influence of the Reflective and Refractive Powers of Bod- 
ies on their Radiation considered. 

24. Hitherto in these investigations no account has been taken 
of reflection at the surfaces of the plates, because 1st, those rays 
only were considered which passed perpendicularly, or nearly so, 
through such plates ; and, 2d, because the indexes of the re- 
fraction for the substances experimented on were not very high. 

But for rays passing obliquely through such media, or for 
rays passing in any direction into substances such as metals, we 
must take account of reflection from the surface which will in- 
fluenoe materially our results. 

Thus, no substance is so opaque for heat as metals, but yet 
only a small portion of the heat falling on them is absorbed, 
the rest being reflected back ; consequently for such bodies the 
radiation (which must be equal to the absorption) is very small. 

It is also desirable, for another reason, to investigate the 
laws according to which the reflective nature of the surface of 



a body influences its radiation. For the question arises, is the 
law of an equal and independent radiation of each particle of a 
body theoretically consistent with equilibrium of temperature ? 
That is, suppose we have an irregularly-shaped inclosure walled 
round with a variety of substances, and each particle of each 
substance radiating into the inclosure, from the sides of which 
it is reflected many times backwards and forwards before it is 
finally absorbed ; this being the case, will the law of equal and 
independent radiation, and those of reflection and refraction, 
so fit with one another, that every particle of the walls of the 
inclosure shall absorb precisely as much heat as it radiates ? 
It will be endeavored to show that these laws are so adapted to 
each other ; and I shall select for the proof a definite form and 
description of inclosure, the conclusions arrived at rendering it 
highly probable (if not rigidly demonstrating) that the same 
adaptation will hold good for every inclosure, however irregular 
or varied. 

For these reasons, I shall now endeavor to investigate what 
connection the radiation of a substance has with the reflective 
power of its surface ; and in doing so (in order to abstract 
entirely from the effects produced by the variable thickness of 
the radiating plate), I shall suppose it to be of indefinite thick- 
ness ; so that all the heat which enters it is absorbed. Our 
consideration is, therefore, limited to the effects of one surface. 

25. Let AB be a portion 

Lam p B!ack of the line of section of an 

indefinitely extended sur- 
face with the plane of the 
paper supposed perpendicu- 
lar to the surface, and let 
this surface belong to a 
body (M) of indefinite 
thickness downwards ; also 
let there be an indefinitely 
extended surface of lamp- 
black parallel to this lower surface, as in the figure. Lastly, 
let the whole be kept at uniform temperature. In order that 
the body (M) may be maintained at this temperature, it is 
necessary that the heat which has left the surface AB, having 



come from the interior of (M), in the direction contaiued*in 
any very small angle CAD, shall be replaced by an equal quantity 
of heat entering the surface AB, to diverge into the interior 
through the same small angle CAD. For, by this arrangement 
it is clear the particles in CAD get back as much heat as they 
give out. 

Part of the heat, no doubt, which fell on A in any direction 
DA, would be reflected back in the direction AD', making the 
same angle with the surface as AD ; but this loss would be 
made up for by part of the heat falling upon A, in the direction 
D'A, being also reflected back in the direction AD. 

The internal reflection at A being compensated for, if the 
heat that really leaves the medium be also compensated for, 
then as much heat will be passing at A in the direction AD as 
will be passing in the direction DA. It will be the same, 
therefore, as if the body, instead of having a surface at A, 
were indefinitely extended upwards from A, as well as down- 
ward ; in which case, as has been already shown (Art. 20), there 
will be equilibrium of temperature, provided that the radiation 
of a particle is equal to its absorption, and that for every des- 
cription of heat. 

Before proceeding further with this investigation, it will be 
necessary to establish some preliminary propositions. 

26. 1st Preliminary Proposition. 

The heat which falls on the line AB in the directions con- 
tained in the very small angle CAD, is 
the same which falls on AE, perpendic- 
ular, EB, through the same very small 
angle. For every ray which fell on AB 
passed through AE, with the exception 
of a small quantity which passed through 
B EF ; but the angle EBF being very 

small, EF is very small compared with AE, and consequently 
the heat falling on EF may be neglected in comparison with 
that falling on AE. 

It is clear, also, that the heat falling on AB is proportional to 
AB, and to the size of the very small angle CAD. 

The above will still hold if, instead of the substance of which 
AB is the surface being supposed below AB, and the rays fall- 



ing on it through a vacuum, we suppose a substance to be 
indefinitely extended upward and the rays to originate in the 
substance itself, and fall on its surface AB. 

For, although any ray GE, which falls on E, will be partly 
absorbed between E and B, it will be as much recruited by the 
united radiation of the particles between E and B as it was 
absorbed ; so far, indeed, as regards quality and intensity (from 
what has been already proved, Art. 20), we may consider such 
a ray to be traversing a vacuum, it being recruited just in pro- 
portion as it is absorbed. 

It is evident, also, that in this case the quantity of heat fall- 
ing on AB will be proportional to the size of the very small 
angle CAD. 

27. 2d Proposition. 

First case. If AB represent a surface (the substance being 

below AB), and OF a surface of lamp- c p G F 

black indefinitely extended (as in Art. 
25), from which rays fall on AB through 
a small angle CAD ; then, if AE be 
drawn perpendicular to GB, the heat 
that falls on AB will = a const. X AE, 
whatever be the value of the angle CAB. 

For, since the angle CAD is exceedingly small, CD may be 
considered very small in comparison with CF or CG ; therefore 
the heat which impinges on AB through the angle CAD may 
be taken to be that which radiates from CG in direction between 
CA and DA; but since the radiative power of lampblack in 
any direction varies as the sine of the angle which that direction 
makes with the surface, this will = const. X AE. Hence, if 
R X CAD be the quantity of heat which falls on AB, when AB 
is perpendicular to GB, that which falls on it when GB makes 
any angle GBA with AB. will be R X CAD sin GBA. 

If i denote the angle which GB makes with the perpendicu- 
lar to AB, then the heat impinging on AB will be R cos i 

2d case. If the substance be above AB, and the rays falling 
on AB originate in the substance, the same formula will hold, 
for it has been shown, in Prop. 1st, that in this case, the heat 
falling on AB through the small angle CAD = that which falls 



on AE through the same small angle; but, since the radiation 
from the interior of the substance is the same in all directions 
(each particle radiating independently and equally in all direc- 
tions), the amount falling on AE will not be aifected by the 
angle which AE makes with the surface; hence the heat falling 
on AB = const. X AE = const. X sin GBA. 

If R' X CAD = quantity which falls on AB when AB is per- 
pendicular to GB, that which falls on it when GB makes any 
angle GBA with AB, will be R' X CAD sin GBA ; also the 
expression corresponding to R cos i' x CAD will be R' cos i' 

28. 3d Proposition. Let a ray strike the surface of a me- 
dium, at an angle of incidence = i; and another ray at an angle 
of incidence i + 6 i, it is required to find the difference between 
the two angles of refraction. 

Let p be the index of refraction, then, 

sin i== fj. sin i' 

Hence, 6 (sin i) = p 6 (sin if) 

cos i 6 i = ft cos i' 6 i' 

TT ., cos i 

Hence, 6 ^ - r,s i 

29. I shall also make the following supposition with regard 
to the laws of reflection and refraction. 

1st. That if Q represent the quantity of heat falling on the 
surface of a medium in any direction CA, and 
0Q be the quantity reflected, then (1 a) Q is the 
quantity of heat refracted into the medium in 
the direction AC 7 . This follows from the law of 
the conservation of vis viva. 

2d. That if the same heat Q originate in the 
Ic 1 medium, and strike A in the direction C'A, 
the quantity reflected back into the medium will be #Q, and 
the quantity refracted out in the direction AC will be (1 a) Q. 

30. These preliminary propositions being established, and 
suppositions made, let us suppose that heat from the surface of 
lampblack strikes the surface AB of the indefinitely thick me- 
dium (Fig. Art. 25) through a small angle 6i (i being the angle 
of incidence), by Prop. 2d. the Quantity of this heat will 



be R cos idi; while the part of it which enters the substance 
we shall call (1 a) R cos i 6 i. These rays will diverge in the 

ff)Q -1 

substance through an angle 6 i'= ^ r 6 i (Prop. 3). 

p COS I 

But the quantity of heat that falls on AB from the interior 
through this angle will be 

R' cos idi' = R' cos i' - u c * s \, *i = ~- cos iti, 

and the portion of this which leaves the medium will be 
(1-a) R' cos ;' di 


Equating this with (I a) R cos 161, which enters the me- 


dium, we have = R or R '= /" R. With this supposition, 


therefore, the law of an equal and independent radiation of 
each particle will give us equilibrium of temperature in the 
particular case under consideration. Had R' been a function 
of i', it would have shown that the law of an equal an inde- 
pendent radiation was inconsistent with equilibrium of tem- 

31. Only part, however, of the heat from the lampblack 
falling on AB entered into the medium, a portion of it = a R 
cos i 6 i being reflected back to the lampblack, hence the total 
quantity of heat radiated and reflected which leaves the surface 
AB through the small angle di will be = R cos i 6 i, the same as 
if the substance had been lampblack, the only difference being, 
that, in the case of lampblack, all this heat is radiated, 
whereas in other substances only part is radiated, the remainder 
being reflected heat. 

32. Although we have considered only one particular case, 
yet this is quite sufficient to make the general principle plain. 
Let us suppose we have an enclosure whose walls are of any 
shape, or any variety of substances (all at a uniform temper- 
ature), the normal or statical condition will be, that the heat 
radiated and reflected together, which leaves any portion of the 
surface, shall be equal to the radiated heat which would have 
left that same portion of the surface, if it had been composed 



of lampblack. And, indeed, we may see, from what has been 
already proved, that should such a state of things only once 
take place, it would always remain, there being no disposition 
to alter it. 

Let us suppose, for instance, that the walls of this enclosure 
were of polished metal, then only a very small quantity of heat 
would be radiated ; but this heat would be bandied backwards 
and forwards between the surfaces, until the total amount of 
radiated and reflected heat together became equal to the radia- 
tion of lampblack.* 

33. The equation R' = //R must necessarily hold for every in- 
dividual description of heat. We have, therefore, two laws 
necessary to the equilibrium of temperature 1st, That the 
absorption of a particle is equal to its radiation, and that for 
every description of heat ; 2d, That the flow of heat from the 
interior upon the surface of a substance of indefinite thickness, 
is proportional caeteris paribus to its index of refraction and 
that for every description of heat. It will, however, be borne 
in mind, that the former of these laws has been verified by ex- 

* This will be clearly seen if we consider only those 

rays that are radiated perpendicular to the surface 
to the case of two parallel plates of polished metal 
~~ of the same description radiating to one another. 
For let r be the common radiation of the point C in direction CD, and 
of the point D in the direction DC, then since these radiations are 
bandied backwards and forwards in the directions CD, DC. until they 
are extinguished, we have the total quantity of heat falling on D in the 
direction CD (if ar denote the proportion of r reflected after one single 
reflection) expressed as follows: 

Total heat radi- J ( r+aV+aV+etc, ) = r(l+a+^+a 8 ) 

ated and reflected, P4 + ar +a 8 r+ B r+etc. f = (since a < 1) 
falling on D, ) ( ) 1 a v 

But 1 a denotes the absorptive power of the metallic surface (all the 
heat not reflected being absorbed). Hence, since the radiative powers 
of bodies are proportional to their absorptive powers (Leslie's Inquiry) 
1 being the absorptive power of lampblack, the perpendicular radiation 

of a lampblack point will be = which is the very same expres- 

1 a 

sion we have obtained for the total heat radiated and reflected together, 
falling on D, in the same perpendicular direction from the metallic 
point C. 



periment, while the latter is only deduced from a theoretical 
investigation. It will also be seen, that by increasing the 
thickness of the radiating plate indefinitely, the radiation be- 
comes ultimately independent of the diathermancy of the plate 
and is regulated only by its refractive index. 

34. The connection which we have attempted to trace be- 
tween the refractive and radiative power of a substance, pre- 
sumes that those rays which we have been considering, have the 
power of forming wave lengths with the medium under con- 
sideration ; that is, of being capable of proper reflection and 

It may be, however, that glass and other similar substances 
are so opaque, with respect to most of the rays of heat of low 
temperature, as to stop them almost entirely at the surface. 

As such rays may, therefore, be conceived to be absorbed 
within the limit of physical surface of the medium, the cor- 
responding radiation may be conceived to proceed from this 
physical surface. To such a case we may perhaps suppose reason- 
ing similar to that of Fourier (as given by Professor Forbes 
in the Philosophical Magazine for Feb., 1833,) to be applicable ; 
the intensity of radiation being therefore proportional to the 
sine of the angle which the direction makes with the surface. 

35. Let us now see, in conclusion, whether these investiga- 
tions seern to point out any connection between internal radia- 
tion and conduction. 

Now, without in the least confirming that these are identical 
there seern to be two points of similarity between them. 

1st, Since the heat which enters metals is all absorbed at a 
very small depth, it follows that the flux of radiant heat from 
within upon the interior of metallic surface is derived from a 
very small depth. 

Also, if we allow (what it has been endeavored to prove, Art. 
30) that the flux of heat upon the interior of the surface is pro- 
portional to the index of refraction, this flux will be greatest in 
the case of metals which may be supposed to have a very high 
refractive power ; besides which, it will, as we have seen, be 
derived from a very small depth. The radiation of a metallic 
particle is therefore very great. 

Now, if internal radiation be in nny way connected with con- 



duction, we might expect that good conducting substances 
should also be good internal radiators of heat, and we see they 
are so. 

2d, The second bond of similarity is this. It seems to be a 
law that substances are almost invariably more diathermanous 
for heat of high temperature than for heat of low ; consequently, 
at high temperatures, the radiation of a thin plate or particle 
of a substance will bear a smaller proportion to the total lamp- 
black radiation of that temperature than at low temperatures. 
The internal radiations of particles of bodies would therefore 
diminish at high temperatures (not absolutely, but with respect 
to the proportion which they would bear to the total radiation 
of these temperatures). If the same rule holds for metals, and 
'conduction be connected with internal radiation, we should ex- 
pect that at high temperatures the conducting power of metals 
would be less than at low temperatures. Now this has been 
proved to be the case by Professor Forbes. 






Transactions of the Royal Society of Edinburgh. 
Vol. XXII, PL I. pp. 5973. April, 1859. 




Division of Subject . \ . . . . . , : 53 

Instruments used and Method of Investigation . . .53 
Effect of Roughening the Surface of a Body upon its Radi- 
ation . . . . . . . . .53 

Nature of the Heat Radiated by Rock Salt . . .56 
Radiation of Glass and Mica at high Temperatures ... 59 
On the Law which Connects the Radiation of a Body ivilh its 

Temperature . . . . . . .s .. .64 

On General Diathermancy . . . . . , .69 






(Read April 18th, 1859.) 

Division of Subject. 

1. The first part of this paper describes the following groups 
of experiments : 

Group I. On the effect which roughening the surface of a 

body produces on its radiation. 
II. On the nature of that heat which is radiated by 

rock salt at 212 F. . 

III. On the radiation of glass and mica, at high tem- 

The second, or theoretical, portion of the paper, has refer- 
ence to the law which connects the radiation of a particle with 
its temperature and to Dulong and Petit's experiments on this 

There is also an addition of a later date than the rest of the 
paper on General Diathermancy. 

Instruments used, and Method of Investigation. 

2. The instruments used, and the method of using them, 
were much the same as described in the first series of these re- 
searches, Art. 3. Should any difference occur in the method of 
conducting a particular experiment, it will be mentioned when 
the experiment so performed comes to be described. 

First group of Experiments Described. 

3. This group of experiments has reference to the effect of 
roughening the surface of a body upon its radiation. This was 



suggested to the writer by Professor Forbes. The first sub- 
stance tried was rock salt. 

A. Rock salt. It was found that roughening the surface by 
means of emery paper, until it became quite dim, had little or 
no effect in increasing the radiation, as will be seen from the 
following statement embodying the mean result of three sets of 

The pieces used were the middle piece (thickness =.36 inch) 
and the thickest piece (thickness = -77 inch), described in first 
series, Art. 6. These pieces were placed at a distance of about 
four inches from the mouth of the polished brass cone, and in 
order to increase the effect, no diaphragm was used. They 
were heated in the boiling-water apparatus already described. 
With this arrangement 

The thick piece gave, when polished, a deviation of .21.! 

when roughened, 21.8 

The middle piece gave, when polished, a deviation of .13.6 
when roughened, 13.5 

4. The next point was to ascertain if roughening had any 
effect upon the quality of heat radiated. 

The following table will show that it does not alter the qual- 
ity of the heat sensibly; its quality being tested by its capacity 
of penetrating a screen of rock salt. 



Percentage of whole 


which penetrates a Rock 
Salt Screen thickness .29 


Rock salt, 

.77 inch thick, 



Rock salt, 

.36 inch thick, 




*In the experiments with roughened surfaces, only one of the sur- 
faces of the substance was roughened, the other being left polished. 
In radiation experiments, therefore, the roughened surface was placed 
next the pile; while in transmission experiments it was placed furthest 
from the pile. 



The trifling difference between polished and roughened salt 
in this table may fairly be attributed to error of experiment. 
We may therefore conclude, that roughening by emery paper 
neither alters the quantity nor the quality of the heat radiated 
by rock salt. 

5. Again, the transmissive power of rock salt for lampblack 
heat of the temperature 212, is not sensibly altered by rough- 
ening the surface. This will be seen from the following state- 
ment : 

The percentage of Lampblack 

heat transmitted was 
With Screen of Rock salt, thick- 
ness .36 inch, polished, 77 

With Screen of Rock salt, thick- * 

ness .36 inch, roughened, 77 

This result naturally follows from the previous one, for it 
has been shown (First Series, Art. 19) that the absorption of a 
plate equals its radiation and since roughening its surface does 
not influence the radiation it ought not to influence the absorp- 

6. B. Glass. It is already known that roughening the 
surface of a plate of glass does not sensibly increase its radia- 
tion. It is only necessary, therefore, to ascertain whether 
roughening the surface of a radiating plate of glass alters the 
capacity of its heat for penetrating a screen of glass. Accord- 
ingly, a plate of crown glass .05 inch thick, 3.75 inches square 
being placed before the cone as a screen, and a similar plate 
roughened, heated in the boiling-water apparatus, being used 
as the source of heat, and no diaphragm used, 

The deviation was 1.0 

When the source of heat was a similar plate, .10 inch 

thick, the deviation became, 1.5 

And lastly, when the source of heat was a plate 

covered with lampblack, the deviation was, 1.9 

With the same sources of heat, only the glass polished in- 
stead of being roughened, these numbers were 0.95, 1.45, 
1.95. From the correspondence between these two sets of re- 
sults, we may infer that the quality of the heat radiated by 
glass (at least in so far as transmission through a plate of glass 



can test it) is not altered by roughening the surface of the 

7. And from all these experiments, we may infer (what has 
indeed been already remarked by Professor Forbes), that 
although roughening its surface with sand or emery paper ren- 
ders a body dim for light yet it still remains specular for heat 
rays, which, possessing a greater wave length than those of 
light, are less liable than the latter to be influenced by scratches 
or furrows. 

Second Group of Experiments Described. 

8. The second group of experiments has reference to 
the nature of the heat which is radiated by rock salt at 212. 
Its quality being tested by transmission through 

a. A screen of mica. 

/?. One of mica split by heat. 

7. One of glass. 

9. a. Mica Screen. By the mean of three sets of experi- 
ments, a mica screen (thickness = .003 inch nearly) passed 
about 31 per cent of ordinary lampblack heat, while it only 
passed 18 percent of rock salt heat. Or if we call the proportion 
of black heat passed by the mica 100, that .of rock salt heat will 
be 58. 

10. /5. Split Mica Screen. Two sets of experiments agreed 
in giving twenty per cent as the proportions of lampblack heat 
of 212, transmitted through a screen of mica split by heat, 
while the proportion of rock salt heat transmitted by the same 
screen was only 15^ per cent. These numbers are to one 
another as 100 to 76. 

11. y. Glass Screen. In order to avoid secondary radiation 
from the screen, which, in this case, absorbs nearly all the 
heat, two screens of microscopic glass were used, the one be- 
hind the other, with an interval between. 

Moreover, as in this case, the proportion of heat transmitted 
is exceedingly small, the following arrangement was adopted to 
make it measurable. 

The experiment consisted of four parts, 

1st. The effect of rock salt heat upon the pile without a 
screen was observed by the ordinary galvanometer. 



2d. The effect of lampblack heat, also without a screen, 
was observed by the same galvanometer. 

3d. The wires of the pile were then transferred to a more 
sensitive galvanometer, and the effect of lampblack heat 
observed, the glass screen being interposed. 

4th. The sensitive galvanometer and glass screen being re- 
tained, the effect of rock salt heat was lastly observed. 

By this method of experimenting, it was merely the relation 
between the diathermancy of the screen for lampblack heat 
and for rock salt heat that was measured; its absolute diather- 
mancy for either of these heats not being determined. Two 
sets of experiments, conducted in this manner, gave the fol- 
lowing result: 

By the first set, calling the proportion of the whole lamp- 
black heat which passed the screen 100, that of the rock salt 
heat which passed the same screen was 54. And by the second 
set, these numbers were 100 to 60. 

12. As in these experiments with a glass screen the propor- 
tion of heat passed is very small, great numerical accuracy 
cannot be looked for and the results obtained are valuable 
rather as determining the direction and character of a fact, 
than as measuring the extent to which it holds. 

13. It is already well known that rays of great ref rangibility 
or small wave length pass through glass and rnica more readily 
than those of an opposite character. The difficulty with 
which rock salt heat penetrates these substances as compared 
with ordinary heat might therefore lead us to infer that the 
wave length of this heat is greater than that of ordinary lamp- 
black heat. 

14. If, therefore, the heat radiated by rock salt is of great 
wave length since (First Series, Art. 19) 'the quality of the 
heat radiated is the same as that of the heat absorbed, it follows 
that the heat most absorbed by rock salt must be heat of great 
wave length; and this derives confirmation from a fact noticed 
by Professor Forbes, viz., that rock salt passes a somewhat 
greater proportion of heat of high temperature than of that of 
low; heat of high temperature possessing a less average wave 

15. If we look now to the relative transmission of the two 



descriptions of heat through mica split by heat, we see that 
the facility of transmission is yet in favor of ordinary heat, but 
not so strikingly as with a screen of common mica. This will 
be seen from the following table : 



Transmission of Or- 
dinary Heat, at 
212 F. 

Transmission of 
Rock salt Heat 
at 212 F. 




Mica split by heat 



Compare this with the following table deduced from the 
results given by Professor Forbes, in the Fourth Series of his 
Researches, Art. 9. 



Transmission of Heat 
from Blackened Brass 
at 700 F. 

Transmission of 
Black Heat 
at 212 F. 

iSlica 015 incli thick 





From a comparison of these two tables, it will be seen that, 
as tested by the two substances, mica and mica split by heat, 
rock salt heat at 212 F bears to ordinary heat of that temper- 
ature a relation similar to that which ordinary heat at 212 F 
bears to heat at 700 F; that is to say, that just as heat of 212 
F has a greater wave length than heat of 700 F, so rock salt 
heat at 212 F has a greater wave length than ordinary heat at 
that temperature. And the surface stoppage produced by 
splitting the mica,* telling most powerfully upon heat of high 
temperature, or small wave length, while the stoppage by sub- 
stance is in the opposite direction, we see how the one effect 
tends, to a certain extent, to neutralize the other, rendering the 
proportions of different kinds of heat passed by split mica more 
nearly alike than those passed by ordinary mica. 

16. All these experiments concur in showing that heat from 
rock salt possesses very great wave length, and probably heat 
from a thin plate of this substance, at a low temperature, may 




be found to possess a greater average wave length than any 
other description of heat which can be exhibited. 

Third Group of Experiments Described. 

17. I now proceed to describe the third group of experiments, 
or those on the radiation of glass and mica at high tempera- 

A. Glass. For the experiments on glass, the following 
apparatus was used: The pile was placed within a box, and 
surrounded with cotton wadding. The orifice through which 
radiant heat was admitted into the box consisted of a brass 
tube AB, blackened in the 
inside. The diameter of this 
tube was inch, its length 3 
inches, and during the 
greater part of its length it 
passed through water, con- 
tained in the chamber CEFD. The side of the box (CAD) next 
the pile was lined with tin foil. Owing tothesmall divergence 
of the rays of heat which hud to pass through the narrow tube, 
the cone might be placed several inches to the left of A without 
sensibly weakening the effect, and, on the other hand, the 
source of heat might be placed some distance to the right of D 
without ceasing to fill up the field of view. By this means, the 
distance between the pile and the source of heat being consider- 
able, no currents of heated air from the latter would be able to 
reach the former; and as the tube AB was blackened in the in- 
side, and passed through water, reflection and secondary radia- 
tion would both be avoided. By means of a lid fitting on the 
tube at A the aperture might be diminished at pleasure. The 
pile was connected with a very sensitive galvanometer. 

When glass at a high temperature was the source of heat, 
a very small aperture was sufficient, and thus the advantage was 
gained of having the whole field covered with glass, all at a 
high temperature, which could not have been the case had the 
aperture been large. 

Slips of glass about inch broad were used, and were set ver- 
tically, just touching a gas flame from a Bunsen's burner. 
When two slips one behind the other were used, the one 



just touched that portion of the flame next the pile, and the 
other that portion furthest from it. A cross section of the 
arrangement is shown on page 59. 

A single slip of glass about .1 inch thick thus heated gave a 
deviation of 16. 5, while two slips, the one behind the other, 
gave 18. 5. When the slips were .05 inch thick these numbers 
were 29 M and36.3. 

18. From these experiments we may conclude, that at a 
high temperature, 700 or 800 F, the radiation from two 
plates of glass, one behind the other, is sensibly greater than 
that from one a result which does not hold for glass at 212. 
Or the fact may be stated thus: 

The radiation of a single plate of glass bears a smaller pro- 
portion to the total radiation of 700 than at 212. 

19. It was next tried whether the capacity of a glass screen 
for passing heat from blackened copper at 700 was altered by 
its being heated. 

In order to ascertain this, blackened copper at 700 F was 
placed behind a slip of glass, and the amount of heat from the 
copper which passed the glass was observed. 

Firstly, When the glass was cold. 

Secondly, When it was heated to between 700 and 800 F. 

20. As in these experiments the considerably fluctuating 
temperature of the source of heat causes a somewhat large 
difference between successive observation, and renders necessary 
a great number in order to arrive at a correct result, it was 
thought desirable, instead of using momentary deviations, to 
employ permanent ones. This was done with complete success; 
the application of the heated copper, or its removal, causing an 
unmistakable alteration of the position of the needle. 

21. The experiment was then varied in the following man- 
ner: The needle was kept permanently deviated by the heated 
glass, and the momentary swing due to the application or with- 
drawal of the heated copper was noticed, and was compared 
with that occasioned by the hot copper when the glass was cold 
and the needle at zero. 

22. These experiments, which are not, perhaps, individually 
susceptible of very great exactness, agreed, however, in render- 
ing it probable that glass, owing to its being heated up to 



about 700 F. does not change its diathermancy for heat of 
700 F. 

23. B. Mica. The experiments on mica were made with 
the ordinary galvanometer. A piece of mica, thickness about 
.008 of an inch, being used as a screen, and a diaphragm, .65 of 
an inch square, at the distance of three inches from the mouth 
of the pile, being employed, the mean of two sets of experiments 
made the proportion of black heat of 200 F passed by the 
mica to be 13 per cent. Placing an additional diaphragm of 
the same size 3| inches beyond the first, and using as a source the 
temperature of 400 F, the mean of two sets of experiments 
made the proportion of heat passed by the mica screen to be 21 
per cent. 

In order to test whether the apparently greater diathermancy 
of the screen for heat of 400 F was owing to the difference in 
the nature of the heat, or to the heat at 400 F striking the 
screen more nearly at a perpendicular incidence, and thus 
experiencing less reflection as well as passing through a smaller 
thickness of mica, an experiment was made on heat at 200 F, 
with the arrangement and distance used for heat of 400 F, 
which seemed to show that this difference of distance does not 
affect sensibly the proportion transmitted. We may therefore 
conclude that the difference in proportions transmitted is ow- 
ing to a difference of quality in the two descriptions of heat. 

24. A cast-iron box was next constructed having this same 
plate of mica inserted as a window, so that, while one side of 
the box consisted merely of a moderately thin plate of cast- 
iron, the other, except round the edges, was composed of mica. 
The cast-iron side was then blackened, and the box filled with 
mercury. A thermometer inserted in the box measures the 
temperature. At 200 F, with the usual diaphragm three inches 
from the mouth of the pile, the proportion between the radia- 
tion of the blackened side and the mica window was, by the 
mean of three sets of experiments, as 100 to 87.8, while at 
400 F, with the usual arrangement of two diaphragms, the 
same proportion was 100 : 84.1. 

25. Let us endeavor to discuss these results. The radiation 
from the mica window consists of three portions : 

a. The proper radiation of the mica plate. 



/?. That portion of the radiation of the mercury which has 
been able to penetrate the mica plate. 

y. That portion of the radiation of the mica which, strik- 
ing upon the mercury, is reflected back by it and has pene- 
trated the mica plate. 

Now, supposing there was no mercury behind the mica, and 
that rnica between 200 and 400 does not alter its diathermancy 
as a screen in any respect, let us inquire what ought to have 
been the result obtained. Then, since the radiation of a thin 
plate equals its absorption (First Series, Art. 19), and since 
the absorption of this mica plate was 8 per cent less at 400 
than at 200 (Art. 23), its proportional radiation ought to be 
8 per cent less at 400 than at 200. 

26. But the effect of the mercury behind the mica mani- 
festly tends to diminish this difference. For we know that 
the mica (Art. 23) passes 8 per cent more of lampblack heat at 
400 than at 200 ; it will therefore no doubt pass a greater pro- 
portion of the heat from the mercury behind at 400 than at 
200. But we have reason to think that the radiation of mer- 
cury is nearly %' of that of lampblack.* Consequently we 
may suppose that owing to this action of the mercury, the pro- 
portional radiation of the mica window at 400 is increased 
about y of 8, that is, 2 percent. This reduces therefore the 
difference from 8 to 6 per cent. 

27. But the mercury acts in another manner also in the 
same direction. Had mercury been a perfect reflector, its 
presence behind the mica would have been equivalent to doub- 
ling the thickness of the plate ; for it would have sent the 
whole radiation of the mica that fell upon it back through the 
mica. But the difference between the proportional radiation at 
200 and at 400 is less for a thick plate of mica than for a thin 
one (indeed, when the plate is indefinitely thick, this difference 
vanishes, and the proportional radiation is the same at all tem- 
peratures); this action of the mercury, therefore, would tend 
still further to diminish the already diminished difference of 

* Provostaye and Desains estimated the proportion of heat reflected 
by mercury to be 77 per cent. The radiation, being complementary to 
this, may be reckoned to be 23 per cent nearly. 



6 per cent. The amount of this action cannot be far from 
3 per cent, * in which case the 6 per cent would be reduced 
to 4 per cent ; now 3.7, or, in round numbers, 4 per cent is the 
observed difference between the proportional radiation of the 
mica window at the temperatures 200 and 400. 

28. We see thus that the behavior of the mica as a screen, 
compared with its behavior as a radiator, agrees very well with 
the supposition which we made in Art. 25; viz., the mica between 
the temperatures of 200 and 400 does not alter its diather- 
mancy in any respect; a result similar to that which we have 
already deduced for glass (Art. 22) between somewhat wider 

29. Experiments with the same object in view, but of a 
more direct description, were made upon mica, similar to those 
already described as having been made upon glass, that is, it 
was endeavored to ascertain whether hot mica passed as much 
heat from hot copper as cold mica; but in these experiments 
the fluctuation was very considerable, probably owing to the 
small body of the mica. Nevertheless, they confirmed the 
results above obtained ; viz., that mica does not change its 
diathermancy in any respect owing to its being heated. 

30. We may therefore conclude that this property (at least 
within moderate limits) is common both to glass and to mica, 
and indeed, a priori, there appears no good reason why the mere 
heating of a substance should change its diathermancy. It is 
the theoretical importance of this property that has induced me 
to take pains to verify experimentally and its importance will 
be seen from some of the consequences which follow its estab- 
lishment, which I shall now proceed to discuss. 

* It would have been better to have tested, by means of a direct exper- 
iment, to what extent the difference between the proportional absorp- 
tion and radiation of mica at 200 F and at 400 F would have been 
diminished by doubling the thickness of the plate; but unfortunately 
the plate of mica was so much cut up by being used as a window, as to 
be unfit for being formed into a double screen. 

We see, however, from Art. 37, that while the difference between the 
proportional radiation of a plate of glass (thickness imm) at 100 C and 
and 390 C is 9 per cent, the same difference for a plate of double the 
thickness is only 7 per cent, or 2 per cent less. We may, therefore, with- 
out much risk of error, adopt this difference of 2 per cent for mica un- 
der experiment. 



On the Law ivhich Connects the Radiation of a Body with its 

31. The experiments of Dulong and Petit upon the cooling of 
two thermometers, one naked, and the other covered with silver, 
seemed to show that the proportion between the radiations of 
these two substances was the same at the different temperatures 
of experiment. 

Now I have endeavored to prove in these researches 1st, 
That the radiation of a thin plate at any temperature equals its 
absorption of black heat of that temperature. 2nd, That the 
diathermancy of glass and mica (and probably of other 
substances) is not altered by heating the substances. Again, it 
is well known that substances are generally more diathermanous 
for heat of high, than for heat of low temperature; it follows 
that the radiation of a thin plate of a substance at a high 
temperature should bear a less proportion to the total radiation 
of that temperature than at a low temperature. 

32. While, therefore, it is likely that the radiation of a 
silvered thermometer (silver leaf being quite opaque for all 
heat) will bear a constant relation to that of a blackened 
thermometer at all temperatures, we should expect that for a 
naked thermometer, just as for the mica window, the radia- 
tion should bear a somewhat less proportion to the total radia- 
tion at a high temperature than at a low. We should therefore 
expect the radiation of the naked thermometer to increase 
somewhat less rapidly with the temperature than that of the 
silvered thermometer. Dulong and Petit, nevertheless, 
found the rate of increase to be the same for both. 

33. Now, in the first place, since glass is exceedingly 
opaque for heat even of 300 C (the highest temperature ex- 
perimented on), the difference we are in search of (analogous 
to the diiference of four per cent in the mica window) would 
be exceedingly small. But, in the second place, Dulong and 
Petit had two thermometers, one of which, containing about 
three pounds of mercury, was used for high, and the other and 
smaller one for low temperatures. This latter circumstance 
will complicate or even vitiate their experiments so far as re- 
gards this peculiar difference we are treating of. 



34. Although, for these reasons, attaching little importance 
to Dulong's and Petit's observations, so far as varying diather- 
mancy is concerned, yet it may be well to state that they show, on 
the whole, a very small difference in the direction which would 
indicate a superior diathermancy of the glass at a high tempera- 

35. Assuming it proved that the proportional radiation of a 
thin plate is less at a high than at a low temperature, I shall 
now endeavor to show that this difference increases as we 
diminish the thickness of the plate. To prove this, it is only 
necessary to exhibit the following table, given by Melloni : 



Thickness of 
Glass Screen. 



at 390 C. 

at 100 C. 
































36. We have already seen that glass does not change its 
properties with regard to heat, by being raised to the tempera- 
ture of 390 C ; it is perhaps, however, too much to conclude, 
that when heated to the temperature of a Locatelli lamp, its 
properties would remain unchanged. At all events, in order to 
make use of the whole of the above table, we may suppose the 
properties of the glass to remain the same throughout, es- 
pecially as the results we shall deduce from the supposition 
will be of the same nature as if we had only extended it to glass 
at 390 C. 

37. Presuming, therefore, that the diathermancy of glass does 
not alter through its being heated, and allowing 4 per cent as 
the proportion of the heat striking it reflected from the first 
surface of a glass screen, and supposing also the same propor- 
tion of the heat which is able to reach the second surface to be 



reflected from it, we may, on the principle that the propor- 
tional radiation of a plate equals its proportional absorption, con- 
struct the following table : 




Thickness of 

Temp, of Lo- 
catelli Lamp. 

Temp, of lu- 

3900 C> 

100 C. 




































38. Let us call the proportional radiation of the glass plate 
at 100 C unity, and we derive the following table. 



Thickness of 

100 C. 

390 C. 

Temp, of In- 

Temp, of Lo- 
catelli Lamp. 







39. We see thus that the radiation of thick plates of glass in- 
creases most rapidly, and that of thin plates least rapidly, as the 
temperature increases, and we may suppose, that if we could 
procure a plate of glass of sufficient tenuity, we might (without 
heating the plate at all), by finding its absorption for heat of 



different temperatures find its radiation at those temperatures, 
which (if the plate were thin enough) would give us the law of 
radiation of a glass particle. This law would not increase nearly 
so fast with increasing temperatures asDulong and Petit's law ; 
it may even be that the radiation of glass particles is propor- 
tional to its absolute temperature. 

40. But all substances (with the exception of black mica 
and black glass, whose peculiarity may perhaps be otherwise ex- 
plained) have the same properties as glass with regard to heat ; 
that is, they are more diathermanous for heat of high than for 
heat of low temperatures. The radiation of thin plates or 
particles of all substances will therefore increase less rapidly 
with temperature than that of black surfaces. It may there- 
fore be, that the same law of radiation is common to very thin 
plates or particles of all bodies ; this law (whatever it be) giving 
in all cases, a less rapid increase of radiation with temperature 
than is indicated by Dulong and Petit's law. Had, however, 
the diathermancy of thin plates of different substances in some 
cases diminished and in others increased for heat of high 
temperature, the law of radiation of a particle could not have 
been the same for all bodies. 

The generality of this law of increased diathermancy of all 
bodies for heat of high temperatures seems, therefore, to me, 
to argue in favor of the universality of the unknown law of 
particle radiation which depends upon the former. 

41. What, then, does Dulong and Petit's law express ? 
The answer is, it expresses the law of radiation of indefinitely 
thick plates, and we have shown that it increases faster than 
the law of radiation of a material particle. 

To facilitate the comprehension of this subject as much as 
possible, I have put it in the following shape. Suppose we 
have two substances opposite one another, the one having the 
temperature of 0, and the other of 100, the latter will of 
course lose heat to the former let us call its velocity 100. 
Suppose, now, that (the first surface still retaining its tempera- 
ture of 0) the second has acquired the temperature of 400 ; 
then we should naturally expect the velocity of cooling to be 
denoted by 400 ; but by Dulong and Petit's law, it is much 
greater. The reason of the increase may be thus explained. 



At the temperature of 100 we may suppose that only the ex- 
terior row of particles of the body supplied the radiation, the 
heat from the interior particles being all stopped by the ex- 
terior ones as the substance is very opaque for heat of 100 ; 
while at 400 we may imagine that part of the heat from the 
exterior particles is allowed to pass, thereby swelling up the 
total radiation to that which it is by Dtilong and Petit's law. 

42. We have thus ascertained 1st, That Dulong and 
Petit's law is not the law of radiation of a material particle ; 
and, 2d, That this law increases less rapidly with the tempera- 
ture than Dulong and Petit's law. But now the question arises, 
can any method be indicated of ascertaining, experimentally 
the law of radiation of a material particle ? Now, by con- 
tinually diminishing the thickness of the plate whose radiation 
at different temperatures we are ascertaining, we certainly ap- 
proach nearer and nearer to the desired law, and, by using the 
method indicated in Art. 37, we may avoid heating this plate 
at all and thus overcome one source of experimental difficulty. 
Yet the thinnest plate we can procure of a substance such as 
glass or mica acts, to all intents, as an indefinitely thick sub- 
stance for a great many of the rays of heat that is, it stops 
them all. The change, therefore, of the unknown law of par- 
ticle radiation into Dulong and Petit's law will to a great 
extent, have taken place even within this very thin plate ; so 
that, in order to reach the desired law or even approximate to 
it, we should have to use much thinner plates than we could pos- 
sibly procure ; and, even without the necessity of heating the 
films, the experimental difficulty and labor of such an investi- 
gation would be very great. 

On the other hand, we may suppose that, since a thin film 
stops so much heat, a portion may be stopped in the physical 
surface of the body, and the absorption might thus influence 
the law of reflection of heat from the surface. The amount 
of this influence depending on the absorptive nature of 
the particles, we might be able to measure the absorption, and, 
consequently, the radiation of the physical surface, that is, of 
a very thin plate. But, in the first place, the difficulties of 
such an investigation would be even greater than in the previ- 


E A D I A T I N A N D A B S R P T I N . 

ous case ; and, in the second place, the true law of reflection is 
not yet finally settled. 

I am therefore induced to think that it is nearly hopeless to 
attempt to ascertain the true law of radiation of a material 
particle, at least by any method of experimenting depending 
upon the use of thin plates, or on the change which absorption 
may be presumed to cause in the amount of heat reflected from 
the surface of a body. 

Edinburgh, March 22, 1859. 

On General Diathermancy (added 15th June). 

43. Circumstances having occurred which may interfere in 
the meantime with my further experiments on heat, I annex 
to this paper an account of some experiments made since the 
day of reading. These were proposed with the view of ascer- 
taining whether diathermancy is confined to rock salt or 
whether bodies partake of this property. If the latter be the 
case, the reason why we have not hitherto ascertained it to be 
so is evidently the difficulty of obtaining crystals of many bodies 
sufficiently large to operate upon ; and if we wish to prove these 
diathermanous we must do so in a way that does not render nec- 
essary the use of large crystals. 

44. Now, a body that is transparent for light, forms, when 
pounded, a white powder or one that reflects a great deal of 
light. It will be granted that the reason of this is because we 
have not only the reflection from the outer surfaces of the 
crystals, but also from many interior surfaces. Now the same 
remark is applicable to heat. A body that is diathermanous or 
transparent for heat should, as a powder, be white for heat, or, 
in other words, reflect it. But (First Series, Art. 31) the re- 
flection plus the radiation of the body at any temperature 
equals the lampblack radiation at that temperature. Hence a 
powdered diathermanous substance ought to radiate less than 
lampblack. Accordingly, different substances having been 
pounded into a fine crystalline powder, made into a paste with 
water, spread on the two sides of parallelopipedons of wood, 
dried and one of the sides, when dry, rubbed over with lamp- 
black, the following result was obtained : 




AT 212 




Table salt 

S3 1 


White su^ar 






Sulphate of potash 



Nitrate of potash . . 



45. Tims we see that table salt being white for heat, the 
radiation of the white side is less than that of the black side ; 
and further, white sugar and alum being both nearly black for 
heat, the radiation of the one side is nearly equal to that of 
the other. We see, moreover, that sulphate of potash and 
nitrate of potash, especially the latter, are white for heat, al- 
though not quite so much so as table salt. May we not there- 
fore presume that these substances are diathermanous ? There 
is, moreover, the following method of confirming the testi- 
mony in favor of the diathermancy of these substances as 
derived from this experiment. 

46. Table salt being white for heat, part of the reflected 
heat will be composed of rays which have been reflected 
from the internal surfaces of crystals. Such rays have there- 
fore been sifted, having left behind that description of heat 
which passes with difficulty through rock salt and also (Art. 
9) through mica. The whole reflected heat from a surface of 
table salt should therefore be of a nature which passes more 
easily through mica than ordinary heat, and (First Series, 
Arts. 31 and 33) since the sum of the reflected and the radi- 
ated heat is equal both in quantity and quality to that from 
lampblack, it follows that the radiated heat from table salt 
(and probably from other substances white for heat) should, in 
order to make up the average quality, have a somewhat greater 
difficulty in passing through mica than ordinary lampblack 
heat. Accordingly, it was found that the diathermancy of a 
mica screen for heat from table salt was less than that for or- 
dinary lampblack heat in the proportion of 92 to 100, while 
it was less for heat from pounded sulphate of potash in the pro- 
portion of 93 to 100, thus confirming the analogy between 



rock salt and sulphate of potash. No such difference was ob- 
served for heat from sugar. 

47. We see also from the above table that the radiation and 
therefore the absorption of table salt is 83.1 per cent, leav- 
ing 16.9 per cent for the reflected heat. Now Melloni found 
that chalk absorbed 56.6 per cent, and consequently reflected 
43.4 percent, of heat from a Locatelli lamp; and if we sup- 
pose table salt to be at least as white as chalk for heat of that 
temperature, we must conclude that table salt is less white for 
heat of 212, than for heat from a Locatelli lamp, following in 
this respect the same law as chalk, which, from being nearly 
black for heat at 212, becomes comparatively white for heat 
from a Locatelli lamp. There is also little doubt that table 
salt reflects more than 16.9 per cent of the light that falls upon 
it. Hence we may conclude generally that powders even of 
diathermanous bodies are less white for heat of low tempera- 
ture than for heat of high temperature and for light. 

48. It would also seem, that, although comparing one 
powder with another, there is no relation between apparent 
whiteness and whiteness for heat, since it was found that very 
white surfaces of pounded sugar and alum (the particles com- 
pressed, not made into a paste with water) reflected little or no 
heat ; yet, comparing powdered surfaces of the same diather- 
manous body together, there seems to be some relation between 
their apparent whiteness and their whiteness for heat, in- 
sufficient pounding, or any circumstance which diminishes the 
apparent whiteness, diminishing also its whiteness for heat. 




BALFOUR STEWART was born Nov. 1, 1828 at Edinburgh. 
He studied at the Universities of St. Andrews and Edinburgh, 
and later entered upon commercial life. His particular taste 
for physical science soon developed itself, however, and we have 
in 1858 a couple of his earliest papers. He became associated 
with Kelland and Forbes at this time and in 1858 contributed 
his most important work on the extension of Prevost's Theory 
of Exchanges in radiation. With the elaborate (at that time) 
facilities at his command he was able to demonstrate the equal- 
ity of the radiating and absorbing power of every substance. 
For this and other work he was awarded the Rom ford Medal 
some years later. In 1859 he was appointed director of the 
Kew Observatory, where for eleven years he directed the im- 
portant studies and investigations carried on there. During 
this period he was seriously injured in an accident from which 
he never recovered. In 1870 he was appointed to the chair 
of Physics in Owens College, Manchester, which he occupied 
until his death Dec. 19, 1887. During this time he issued 
his well-known texts in Physics. His " Conservation of 
Energy," " The Unseen Universe" (in conjunction with Tait), 
his experiments on the viscosity of ether, etc., all illustrate the 
comprehensiveness of his mind and the originality of his 







Reprinted from " Investigations on the Solar Spectrum and 
the Spectra of the Chemical Elements," 2d. Edition, Berlin, 
Ferd. Dummler's Publishing House, 1866, Gesammelte Abhand- 
lungen, pp. 571-598, Leipzig, 1882. 





Nature of Heat Rays and Light Rays . . . . 75 

#/#6'& Bodies defined . . . . . . . . 76 

Definitions . . -. . . . .. . . . 77 

Ratio between the Emissive and the Absorptive Poiver . 78 
Proof of the Law of Emission and Absorption for Black 

Bodies .: 78 

Proof of the Law of Emission and bAsorption for Any 

Body , . 89 

Generalization of the Law of Emission and Absorption . 92 

Some Results of the Law , . ' . ' . . . 94 






HEAT rays have the same nature as light rays ; these con- 
stitute a special class of the former. The invisible heat rays 
are distinguished from light rays only by the period of vibra- 
tion or the wave length. All heat rays follow the same laws 
in their propagation, which are known for light rays. A 
luminous body in space sends out light rays that are indepen- 
dent of the bodies on which they fall ; similarly all heat rays 
which a body sends out are independent of the bodies which 
form its environment. 

Of the heat rays that are sent out to a body by its surround- 
ings a part are absorbed, the others are sent on in directions 
which are varied by reflection and refraction. The rays re- 
fracted and reflected by it pass off along with those sent out by 
it, without any mutual disturbance taking place. 

Through the radiations which a body sends out, the quantity 
of heat which it contains will, according to the law, sustain a 
loss which is equivalent to the vis viva of those rays and, 
through the heat rays which it absorbs, a gain which is equiv- 
alent to the vis viva of the absorbed rays. But in certain cases 
an exception to this rule may occur, in that the absorption and 
the radiation produce other changes in the body, as for ex- 
ample in bodies which are chemically changed by light, and 
light absorbing media which lose their power of shining 

1 Investigations on the solar spectrum and the spectra of the chem- 
ical elements, 2d. Edition, Berlin, Ferd. Dummler's publishing house 




through the radiation of the light which they have absorbed. 
Such cases should be excluded on the assumption that neither by 
means of the rays which it radiates or absorbs, nor by means of 
other influences to which it is exposed, does the body possess the 
power to undergo a change, if its temperature is kept constant by 
the addition or the subtraction of heat. Under these conditions, 
according to the law of equivalence of heat and work, the 
amount of heat which must be transferred to a body in a given 
time to prevent cooling, which would occur in consequence of 
its radiation, is equivalent to the vis viva of the emitted rays ; 
and the amount of heat which must be withdrawn in order to 
counterbalance the heating from absorption of radiations, is 
equivalent to the vis viva of the absorbed rays. 

Let a body which satisfies these conditions be surrounded by 
an enclosure, having the same temperature, through which no 
heat rays can penetrate, whose temperature is kept constant 
and which satisfies the same conditions. The body sends out 
heat rays and is encountered by such heat rays, which, in part, 
proceed from the enclosure, in part, are thrown back to the 
same by reflection from it, absorbing a part of them. Its tem- 
perature must thus remain the same, unless heat is withdrawn 
from it or communicated to it as follows on the principle from 
which Carnot's law results. For this reason, the vis viva of 
the rays, which it sends out in a certain time, must equal the 
vis viva of the rays which it absorbs in the same time. 

The proof which rests upon this conclusion requires the ac- 
curate investigation of the rays that travel back and forth be- 
tween the body and the enclosure. This investigation will be 
much simplified if we imagine the enclosure to be composed, 
wholly or in great part, of bodies which, for infinitely small 
thickness, completely absorb all rays which fall upon them. 

I will call such bodies perfectly black, or more briefly black. 
A black body, in this sense of the word, must have the same re- 
fractive index as the medium in which the radiation takes 
place ; then there will be no reflection at its surface, and all in- 
cident rays will be wholly absorbed. Thick iodine vapour in 
contact with air, or pitch in contact with glass, may be treated 
as black bodies, approximately, but not iodine vapour in con- 
tact with glass or pitch in contact with air. Next, the radia- 



tion in empty space will be investigated ; the Mack bodies re- 
ferred to must therefore have a refracted index which differs 
only infinitely little from 1. 

The assumption that such black bodies are conceivable forms 
an important aid in the proof which will be presented here. 
Further, it will be assumed that perfectly diathermanous 
bodies are conceivable, that is, such which will absorb none of 
the incident heat rays of whatever nature these may be, and 
finally, that a perfect mirror is conceivable, i.e., a body which 
reflects completely all heat rays. A perfect mirror, like every 
diathermanous body, can itself send out no rays ; for if it did 
(confined in an enclosure of like temperature) it would warm 
this enclosure more and more and cool itself more and more. 

o n 


Before a body C, Figure 1, imagine two screens, /Si and Sz placed 
in which are two openings 1 and 2, whose dimensions are infi- 
nitely small with respect to their distance 
apart, and each of which has a center. s * 

Through these openings passes a pencil 
of rays sent out by the body C. Of this 
pencil of rays, let us consider the part, 
whose wave length lies between A and 
/i-j-rJA, and let this be divided into two n 

polarized components, whose planes of 
polarization are the planes a and b per- 
pendicular to each other, passing through 
the axis of the ray pencil. 

Let E&\ be the intensity of the com- 

ponent polarized in a, or, what is the same thing, the increase, 
which the vis viva of the ether beyond the screen S% experiences 
through this component in the unit of time. The quantity 
E is called the emissive power of the body C. 

Conversely, upon the body C there falls through the open- 
ings 2 and 1 a pencil of rays having the wave length A, polar- 
ized in the plane a; of this, the body absorbs a part while it 
reflects or transmits the remainder ; let the ratio of the inten- 


sity of the absorbed rays to the incident rays be A and let this 
be called the absorptive power of the body C. The quantities 
^and A depend upon the nature of the condition of the body 
6', besides also upon the form and position of the openings 1 
and 2, the wave length A and the direction of the plane a. 


Under these conditions the following law holds : The ratio be- 
tween the emissive and the absorptive power is the same for all 
bodies at the same temperature. 

This law will be proven, first, for the case where only black 
bodies are compared with each other, that is, those whose 
absorptic power = 1 ; i. e., it will be shown that the radiating 
power of all black bodies is the same at the same temperature. 

The proof of this special law is similar to that of the general 
law, but simpler ; it will therefore facilitate the understanding 
of the latter. Moreover, conclusions which are drawn from 
the special law will be used in the proof of the common law. 


Proof of the Law 3 for Hack bodies. 

Let (7 be a black body ; let its emissive power, which is com- 
monly indicated by E, be called e ; it will be proven that e 
remains unchanged, when C is replaced by any other black 
body of the same temperature. 

Imagine the body C' enclosed in a black covering, of which 
the screen 82 forms a part, let the second screen 182, like the 
first, be made of black substance and let both be united with 
each other on all sides by black walls, as shown in Figure 2. 
Suppose the opening 2 to be closed at first by a black surface, 
which I will call surface 2. The whole system must have the 
same temperature and the covering be maintained at a constant 
temperature throughout. According to the statements made 
in Figure 2, 1, the vis viva of the rays which the body C" sends 
out in the given time, must then equal the vis viva of the rays, 
which it absorbs in the same time ; in other words : the sum of 
the intensities of the rays which it sends out must equal the sum 
of the intensities of the rays which strike it, since according to 



supposition it completely absorbs the latter. Now suppose the 

surface 2 removed, and the opening closed by a portion of a 

perfectly reflecting spherical surface, placed directly back of it 

and having its center at the middle point of the opening 1. 

Equilibrium of temperature will then exist. There must also 

be equality between the intensity of the rays which the body C 

sends out, and of those incident upon it. Since the body C 

now sends out the same rays as in the cases 

previously considered, it follows that the 

intensities of the rays incident upon C are 

the same in both cases. By the removal of 

surface 2 the rays are withdrawn from C 

which pass through opening 1 ; therefore 

the concave mirror placed at opening 2 

throws just the same rays back to C which 

this sends out itself through the openings 

1 and 2, for the concave mirror forms from 

opening 1 an image which coincides with 

itself. 1 

The law given would therefore be proved 

if all rays of the two pencils compared have the wave length 
\ and are polarized in the plane a. Both pencils of rays, 
however, are made up of different components and form the 
equality of the intensity of the whole pencil. "We may not 
directly infer the equality of the intensity of corresponding 

The necessary completion of the proof may easily be given 
when a plate is supposed to exist, having the property of trans- 
mitting undiminished rays whose wave length lies between a 
and A + <tt. and whose plane of polarization is parallel to the 
plane a; but which completely reflects rays of other wave 

1 The diffraction of the rays at the edges of opening 2 may he neg- 
lected, since the openings 1 and 2 may be assumed infinitely small with 
respect to their distance and yet infinitely great with respect to the 
wave length, that is, so great, that the defraction may be inappreciable. 

From this it follows that the intensity of the pencil of rays, which the 
body C sends ont through openings 1 and 2, equals the intensity of the 
pencil of rays which the black surface 2 sends out through the opening 
1. Since this intensity is independent of the form and further character 
of the black body C, so, likewise, is the former. 



lengths or of an opposite polarization. If we should imagine 
the arrangement shown in Figure 2 modified by bringing such 
a plate before opening 1, then we may immediately arrive at 
the law to be proved by the treatment employed in respect to 
this figure. 

The assumption that such a plate is possible is in no wise 
justified. On the contrary, a plate is possible which, of the 
rays striking it at the same angle, transmits and reflects them 
in different degrees according to their wave length and plane 
of polarization. A plate, which is so thin that the colors of 
thin films are visible and which is placed obliquely in the path, 
shows this. 

Such a plate is required for the investigation under consid- 
eration in order to compare them. Besides this, it is necessary 
to make such an arrangement that both pencils of rays do not 
pass through the plate, but are reflected from it at the polariz- 
ing angle, the plane of reflection coinciding with the plane a. 
This is advantageous in as much as the rays polarized perpen- 
dicularly to a need not be considered. Further, the plate must 
be made of a perfectly diathermanous medium, it will then 
absorb no rays and send out none. 


In the arrangement described in Figure 2 imagine a plate of 
s 2 the kind described and designated as P, 

brought between the openings 1 and 2 (Fig. 
3). Let it be so placed that the pencil of 
rays passing through the openings 1 and 2 is 
incident at the polarizing angle and the 
plane of incidence is the plane a. Let the 
wall which unites the screens Si and 83 be 
so shaped that the image, which the plate 
P casts from the opening 2 lies within it ; 
in the place and of the form of this image 
imagine an opening which I will call open- 
ing 3. Let opening 2 be closed by a black 
surface of the temperature of the whole 
system, and let opening 3 be closed in the first place by a 
similar surface, and in the second place by a perfect concave 



mirror having its center where the plate P forms the image of 
the middle of opening 1. In both cases the equilibrium of 
temperature is maintained ; through consideration given in 
the preceding paragraph, it follows therefore that the sum of 
the intensities of the rays, which the body C is deprived of 
through the removal of surface 3 equals the sum of the inten- 
sities of the rays which are brought to it through the agency 
of the concave mirror. Let a black screen SB (of the temper- 
ature of the whole system) be so placed that none of the 
rays which surface 3 sends out are directly incident upon 
opening 1. The first sum, then, is the intensity of the rays 
which proceed from surface 3, and are reflected by plate P and 
pass through opening 1; they will be designated by Q. The 
second sum is made up of two parts ; one component comes 
from C and is : 


d/.er 2 


where r represents a quantity dependent upon the nature of 
the plate P and the wave length A; the second part consists of 
rays which have come from a portion of the black wall which 
unites the screen S l and $ 2 ,have passed through the plate P 
and been reflected from the concave mirror, and then from the 
plate P; this part will be designated as R. It is unnecessary 
to examine further the value of R; it suffices to notice that R, 
as well as Q, is independent of the nature of C. Between the 
magnitudes introduced there exists the equation : 

:/eV 2 -f- R = Q 

If we now imagine the body C replaced by another black 
body of the same temperature, letting e indicate for this what 
e has represented for the other, there exists the equation 


<T/e'r 2 -f E = Q 

From this it follows that 

dl. (ee') r' 2 = 

Let us now assume that the index of refraction of the plate P 



differs but little from unity. From the theory of the colors of 
thin plates it follows then that we can place 

r = p sin 2 -?- 


where p represents a quantity proportional to the thickness of 
the plate P, independent of A, and a quantity independent of 
this thickness. From this follows the deduced equation : 


' Since this equation must hold for every thickness of the 
plate P> and hence for every value of p, it follows that for 
every value A we may conclude that 

To prove this, substitute in that equation for sin* ~- : 


i(cos4 ~ 4 cos 2 ~ _i_Q) 

A A ' ' 

and differentiate twice with respect to p : we then have 

4 -f- cos 2 f- ) = 

In place of A let us introduce a new quantity into the equa- 
tion ; where 



and set 

we thus obtain 


daf (a) (cos 2 p a cos p a) =0 

If we consider that when (a) represents any arbitrary func- 
tion of a 

J /* a 

da? (a) cos 2 pa = I da<j> ( -~- ) cos pa 
o *J o 

from which we may conclude that if we substitute for c , we 
may therefore write 

00 a 

d* \f( g- ) 2/ (a)] cos p a = 



Multiply this equation by dp cos xp, where x represents an arbi- 
trary quantity, and integrate it from p = to p = oo. Accord- 
ing to Fourier's formula which is expressed by the equation 

/* C** TT 

I dpcospx I da^ (a) cos pa = $ ( x ) 
Jo Jo 2 

we have 

OP /(-I. ) = 2/(a) 

From this it follows that /(a) either vanishes for all values 
of a, or becomes infinitely great when a approaches zero. When 
a approaches zero A becomes infinite. If we remember the 
meaning of /(a) and consider that p is a proper fraction, and 
that neither e nor e' can become infinite when A increases to 
infinity, then it is evident that the second case cannot exist 
and therefore, that for all values of A, e = e'. 

In a similar way we may treat the case when C is not a black 
body but is an arbitrary one. We shall not assume for the 
same that it is homogeneous ; partly on its surface, partly in its 
interior will the rays therefore, which are incident upon it from 
the black envelope, experience the most manifold modifications. 
On these grounds, there must be, as a preliminary to the pro- 
posed proof, a study made of the radiation which takes place 
between black surfaces of the same temperature, for arbitrary 
bodies. To this investigation, which depends upon the formula 
just proved, the following paragraphs are devoted. 


If the pencil of rays which the body C sends out through 
openings 1 and 2 should be partly linearly polarized, the plane 
of polarization of the polarized portion must rotate when C is 
rotated around the axis of the pencil. Such a rotation must 
therefore change the value of e. Since, according to the equa- 
tion proved, such a change cannot take place, the pencil of 
rays can have no linearly polarized portion. It can be proved 
also, that it can have no circularly polarized part. But the 
proof for this will not be given here. 

We will also grant, without this, that black bodies are con- 



ceivable in whose structure there is no reason why they should 
send out in any direction more right handed circularly polarized 
rays than left handed circularly polarized rays. 

Of this character will the black bodies, concerned in the fur- 
ther treatment, be assumed ; they send out in all directions 
unpolarized rays. 

o ty 

The quantity represented by e depends, aside from the tem- 
perature and wave length, on the form and the relative position 
of the openings 1 and 2. If w\, w? represent the projections of 
the openings upon planes perpendicular to the axis of the pen- 
cil, and if s is called the distance of the openings, then 

where /is a function of the wave length of the temperature 


Since the form of a body C is arbitrary, a surface may be 
substituted, which exactly fills opening 1 and which I will call 
surface 1 ; the screen Si may then be imagined removed. Fur- 
ther the screen $2 may be considered removed if the pencils of 
rays which e covers, is defined as that which falls from surface 
1 upon surface 2, which the opening 2 exactly fills. 


A consequence of the last equation, which immediately fol- 
lows and which will later be used, is that the value e remains 
unchanged if we imagine the openings 1 and 2 interchanged. 

We will now establish a law which may be treated as a gen- 
eralization of the law presented in the last paragraph. 

Between the two black surfaces of the same temperature 1 
and 2, is placed a body which may refract, reflect, or absorb in 
any way the rays which one sends to the other. Several pencils 
of rays may pass from surface 1 to surface 2 ; choose one of 
these, and consider the part of the one at 1 whose wave length 
lies between A and A -f eZ/i, and divide this into two components 



whose planes of polarization are the planes of a\ and b\ which 
are perpendicular to each other (otherwise arbitrary). Let the 
part of the first component which enters 2 be divided into two 
components whose planes of polarization are the planes a 2 and 
b 2 perpendicular to each other (otherwise arbitrary). Let the 
intensity of the component polarized in 2 be Kd'k. Of the 
pencil of rays which passes over the same path as the preceding 
one, from 2 to 1, let us consider the part at 2 whose wave 
length lies between A and a + dA, and divide this into two com- 
ponents polarized in # 2 and Z> 2 . Divide the portion, which 
reaches 1 from the first component, into two parts whose planes 
of polarization are a\ and b\. Let the intensity of the com- 
ponents polarized in a\ be K'd'\. Then 

The proof of this law will be made upon the assumption that 
the rays under consideration undergo no weakening in their 
path, and also upon the assumption that refraction and reflec- 
tion occur without loss, that there is no absorption and that 
the rays, coming from 1, polarized in a\, reach 2 polarized in 2 , 
and vice versa. 

Through the middle point of 1 pass a plane perpendicular to 
the axis of the pencil of rays, either incident or emergent at 
this point, and imagine in this a right-angled coordinate sys- 
tem, whose origin is that middle point. Let 
x\ y\ be coordinates of any point in the plane, 
Figure 4. At the distance of unity from this 
plane, imagine a second, parallel to it, and iu 
this, a coordinate system whose axes are parallel 
to each of those, and whose origin lies in the 
axis of the pencil of rays. Let Xs y$ be coordi- 

nates of any point in this plane. In a similar 
FIG. 4. manner pass through the middle point of 2, a 

plane perpendicular to the axis of the bundle of rays, incident 
or emergent at this point, and introduce in this, a rectangular 
system of coordinates whose origin is the middle point men- 
tioned. Let x 2 y<2 be coordinates of a point in this plane. 
Finally, at a distance of unity from this plane and parallel to 
it imagine a fourth, and in it a system of coordinates whose 
axes are parallel to the axis of x*, y? and whose origin lies in 



the axis of the pencil of rays. Let x, y be coordinates of any 
point in this fourth plane. 

From an arbitrary point let a ray pass to any other point 
(#2, #2) ; let Tb& the time required to pass from one point to 
the other ; we will suppose it to be a known function of x\, y\, 
#2, y<2> If the points (x 3 , y 3 ) and (x, y*) He in the path of the 
ray referred to, (and if for the sake of brevity the velocity of 
the ray in vacua be taken as unity) the time which the ray re- 
quires to pass from (x 3 , y 3 ) to (z 4 , y*) will be 


Assuming the points (#3, 2/3), (#4, y 4 ) given, and the points 
(a?i, y\), (#2 #2) required, we could find these from the condition 
that the above expression is a minimum. If we assume that 
the eight coordinates x\, y\, x 2 , y 2 , x 3 , yz, x, y are infinitely 
small, the following equations express the condition that the 
four points (x\, #1), (z 2 , 2/2), (#3, #3), (x, ?/ 4 ) lie in one ray : 

dx l ' dx 2 

dT dT 

Now let (xi,yi) be a point in the projection of surface 1 on the 
plane Xi, y\ and let dx\ 9 dy\ be an element of this projection in 
Ayjiich the point Xi, y\ lies and which is infinitely small with 
respect to the surfaces 1 and 2. Let (x 3 , y 3 ) be a point in a 
ray proceeding from (x\, y\) to surface 2, dx 3 , dijs, a surface 
element in which the point (x 3 , y 3 ) lies, of the same order as 
dx\, dy\. The intensity of the rays of the required wave 
length and of the given plane of polarization, which, proceed- 
ing from dx\, dy\, pass through dx 3 , dy 3 , is then according 

d\ I dx\ dy\ dx 3 dy 3 . 

According to the supposition, this amount of rays reaches 
surface 2 undiminished and forms an element of u quantity des- 
ignated by Kdh. JTis the definite integral 



/ f f f f 

\s \s \s */ 

The integration here with respect to x%, ?/ 3 is to be taken 
over those values which these quantities have according to the 
above equations, while x\ and y\ remain constant and x 2 ,i/2 have 
all the values which correspond to the projections of surface 2 
upon the plane # 2 , y 2 . The integration with respect to x\, y\ 
is then to be taken over the projection of surface 1. The 
double integral 

dx 3 dys so limited, 

y y 

is, however, 

/* /* / 

or from the equations for z 3 , f/ 3 

C r / ^' 2y t) 2 r ^ 2 r _ __ 

/ / \^Xj fix 2 by i by 2 '^ '*'" ' x/> / * / " * ^^' 

where the integration is taken over the projections of surface 2 

C C C/ tfT fPT ^T tfT \ 

)dxidyi dx 2 dy% 

where the integration is taken over the projections of surfaces 
1 and 2. 

If the magnitude of a K' be treated in the same way, remem- 
bering that a ray requires the same time to pass over a path be- 
tween two points in either direction, the same expression 
will be found for K' as for K. Thus, the enunciated law is 
proved, subject to the limiting conditions under which it will 
next be proved. This limitation may, however, be immediately 
disposed of by an observation made by Helmholtz in his 
"Physiological Optics," p. 169. Helmholtz says here (with 
somewhat different notation) : " A light ray passes from point 
1 to point 2 after any number of refractions, reflections, etc. 
Through 1 suppose two arbitrary planes a\ and #1 passed in the 
direction of the ray perpendicular to each other, in which its 
vibrations are supposed to be resolved. Two similar planes, 2 
and #2 are also passed through the ray at 2. Then the following 



may be proved : If a quantity i of light polarized in the 
plane a\ proceeds from 1 in the direction of the ray mentioned 
and of this, the quantity k of light polarized in the plane a\ 
reaches 2, so will vice versa the quantity k of light polarized in 
# 2 reach point 1 if the quantity i of light polarized in a 2 
proceed from point 2." 1 

Applying this law, and representing by 7 the value of the 

ratio 4 for the two rays which pass in either direction between 

the points (x\, y\) and (# 2 , 3/2), then an expression is obtained for 
K &s well as for K which differs from that formed only in that 
now y appears as a factor under the integral sign. 

The equality of ./Tand 7T' exists accordingly when > has a 
different value for the rays into which one of the pencils com- 
pared may be divided ; for example, it is unaffected if a part of 
the pencil is intercepted by a screen. 

Of the same pencils which were compared in the preceding 
paragraphs, the following law also holds : of the pencil passing 
from 1 to 2, consider the part at 2 whose wave lengths lie be- 
tween A and A + dl and resolve this into two components polar- 
ized in 2 and #2 ; let the intensity of the first component be 
Hd'k. Of the pencil which passes from 2 to 1, consider at 2 the 
portion whose wave lengths lie between A and A + d% 9 and resolved 
this into two components polarized in a 2 and Z 2 . Let the por- 
tion of the first component reaching point 1 be H'd\. 

Then H=ff'. The proof of this law is the following ; 
^and K are to have the same meaning as in the preceding 
paragraph ; let L and L' be the quantities which arise form K 
and K'. when plane a\ is interchanged with plane bi. 

1 The law of Helraholtz, as he himself noted, does not hold good 
when the plane of polarization of a ray undergoes any rotation, such as 
magnetic force produces according to Faraday's discovery ; therefore, 
in the following considerations magnetic force must not be considered 
as present. Helmholtz limited his law also by supposition that light 
undergoes no change of refrangibility such as occurs in fluorescence ; 
this limitation is unnecessary in the application of the law, if rays of 
only a given wave length are regarded. 



Then L = L' } similarly K = K', further H K+ L, because 
rays polarized perpendicularly to each other do not interfere, 
when they are brought back to a common plane of polarization 
in case they are a part of an unpolarized ray ; and according to 
6 the surface 1 sends out unpolarized rays. 

Finally H' = K+ L', because two rays, whose planes of polar- 
ization are perpendicular to each other, do not interfere. 
From these equations it follows that H= H'. 

Let Fig. 2 have the same meaning as in 4, only let the body 
C be not a black body but an arbitrary one. Let opening 2 be 
closed by surface 2. This surface sends out a pencil of rays 
through opening 1 to the body C, which is partly absorbed by 
this body, and partly scattered in different directions by reflec- 
tion and refraction. Of this pencil consider the part between 
1 and 2 whose wave lengths lie between A and A + d\ and resolve 
this into two components polarized in plane a and the plane 
perpendicular to this. Let that part of the first component 
which escapes absorption by C, and hence strikes the black cov- 
ering in which the body C is inclosed, be M'd"k. A certain por- 
tion of the rays which a part of the covering sends out to the 
body C, fall upon surface 2 through opening 1 ; thus by means 
of the body C a pencil of rays is produced which passes through 
opening 1 to the surface 2. Of this, consider the part whose 
wave lengths lie between A and A + dh and divide it into two 
components polarized in plane a and the plane perpendicular 
to it. Let the intensity of the first components be Md\. 

Then M= M '. The truth of this law follows from the propo- 
sition from the preceding paragraph, if we apply this to all 
pencils of rays, which surface 2 and all the elements of the 
black cover surrounding the body C interchange with each 
other by means of the body C, and then form the sum of the 
equations so obtained. 


Proof of the proposition # for any body. 
Let the arrangement shown in Fig. 3 and described in 5 be 


taken, only let the body C no longer be a black body, but ar- 
bitrary. Ill both cases described there, the equilibrium of heat 
subsists ; then the vis viva which is drawn out from the body 
G by the removal of the black surface 3, must therefore be 
equal to the vis viva which is supplied to this by the presence 
of the concave mirror. The symbols used in 5 will be used 
here with the same meaning. The letters E and A will have 
the meaning given them in 2. 

If surface 3 is removed, then the rays are withdrawn from 
the body C which this surface sends to it ; the intensity of the 

x 00 

part of these rays which it absorbed is = f cUer A. 

*/ o 

Now the rays must be examined which are transmitted to 
the body by the presence of the concave mirror. All these rays 
must be reflected from the concave mirror to plate P and from 
this to opening 1, and these must pass in the same direction as 
if they came from opening 2. Before they strike the concave 
mirror, they have either experienced a reflection from it or not. 
In the first case they can only be sent back again to the con- 
cave mirror by means of the body (7 over the path which is the 
reverse of that already described. It must next be premised that 
the body (7 has such a position that, of the rays which pass to 
it through 2 and 1, only an infinitely small part will be re- 
flected back again through opening 1 to opening 2. Then, of the 
rays in question, only an infinitely small fraction have suffered 
multiple reflection at the concave mirror, audit is sufficient to 
consider those which are reflected only once at the mirror. Of 
these, a part proceed from the body (7, the rest from the black 
covering. The first part has experienced a double reflection at 
plate P ; the vis viva which the body absorbs from it is 


The second part which proceeds from the black enclosure 
may again be considered as consisting of two parts ; one which 
passes to the concave mirror without the mediation of the body 
C., and a second, by means of it. Each arises from rays which 
proceed from black partition opposite the concave mirror, 
and have passed through the. plate P, have been reflected from 
the concave mirror to the plate P and from this to opening 1. 



Without examining from which part of the black wall these 
rays have proceeded, their intensity may be found by the law 
established in 11. 

By the application of this, the intensity of those rays which 
were absorbed by the body C is shown to be 


(/ACT (1 r)A. 

Finally in order to find the intensity of the rays which proceed 
from the black covering by means of the body C to the concave 
mirror, and pass back from this to the body C and are here 
absorbed, let N designate the quantity which the quantity in- 
dicated by M in 12 becomes in consequence of plate P being 
brought into its place and the surface 3 removed ; the intensity 

is then = f MNr* A. 

J o 

The difference between M and N arises only from .the varia- 
tion which the rays, falling upon the body C from the black 
covering through opening 1, undergo by the introduction of 
plate P and the removal of surface 3. Suppose the plate P 
brought into its position, without removing surface 3, then M 
can undergo no change, since all the pencils of rays, which go 
to the opening 1 remain unchanged ; the pencil proceeding 
from surface 2, for example, suffers a loss through reflection at 
plate P which will be exactly replaced by the reflection of the 
rays going out from the surface 3. The difference MN is 
therefore only produced by the removal of surface 3 and is also 
equal to the part of M which arises from the rays sent out by 
surface 3 to opening 1 by means of plate P. According to the 
supposition made in these paragraphs concerning the position 
of the body C, MNis infinitely small in comparison with the 
intensity of the rays of equal wave length which surface 3 
sends to opening 1 by means of plate P, as well as infinitely 
small in comparison with the intensity of rays of equal wave 
length and polarized in the plane a, which surface 2 sends to 
opening 1 by the absence of the plate P, and therefore finite 
and also infinitely small with respect to the quantity repre- 
sented by M ' in 12 (assuming that 1 A is not infinitely 
small). Since, however, as already pointed in the places cited, 
M' = M , we may also place 




But according to the definition given of M' 
M' = e (1 A) and therefore 


dA Nf 2 A = I eZ/e ( 1^ ) r 2 A. 
o y o 

The proposition presented at the beginning of this paragraph 
would then be expressed by the equation : 

JOO x00 sCO x00 

o */ o */ o */ o 

or by the equation f ^ (EAe) Af 2 = 0. 

J o 

By the same treatment employed in 5 with reference to a 
similar equation, we may conclude that for every value of A* 

- =e 
or substituting for e its value in 7. 

E_ _ j Wi W% 
A = 82 * 

Thus, the law 3 is proved under the assumption that, of the 
pencil which falls from surface 2 through the opening 1 upon 
the body (7, no finite part is reflected by this back to the 
surface^ ; further, that the law holds without this limitation, 
if we consider that when the condition is not fulfilled, it is 
only necessary to turn the body C infinitely little in order to 
satisfy it, and that by such a rotation the quantities ^and A 
undergo only and infinitely small change. 

A Generalization of tlie Laiv 3. 

The discussions given assume that the space in which the 
radiation occurs is a vacuum. But the same treatment also 
obtains when this space is filled with any perfectly diather- 
manous medium ; only the function / will then be different 
than in the former case. The symbol /may then be retained 
for a vacuum and /' may be called the corresponding function 
of temperature and wave length for a certain diathermanous 
medium ; if n is the index of refraction of the same for the 



temperature and wave length to which / and /' refer, then a 
simple relation exists between I', I, and n ; the same follows 
from the law already demonstrated as will be here shown. 

Imagine a layer of a diathermanous medium bounded by two 
parallel planes, and with one side in contact with the black sur- 
face F. Let the thickness of the layer= 1. For this body, the 
s , absorptive power of A , and the emis- 
sive power E, in relation to a certain 
pencil of rays will be investigated. 
The opening 1 and 2 which determine 
the form of the pencil will be in 
screens S\ and $ 2 , of which the first 
covers the surface of the layer hither- 
tofore supposed to be free, and the sec- 
ond is parallel to it; let the line 
FIG. 5. joining the middle points of the open- 

ings be perpendicular to the screens. Of any pencil of rays 
of a definite wave length and direction of polarization, which 
passes from the opening 2 to the opening 1, a fraction will be 
reflected at the latter which may be designated by p ; the rest 
passes to the surface J^and is here completely absorbed ; there- 

To find E, represent by x, y ; x\, y\ ; and # 2 , y<* the coordi- 
nates of a point of the surface F, the opening 1, and the open- 
ing 2, reckoned from those points which are found in the axis 
of the pencil. If these points lie in a ray, then if s again rep- 
resents the distance of the two openings, 

must be a minimum with respect to x\ and y\ : i. e., 

x = Xl - x ^- x i y = yi y*-yi 

ns > ns 

if w\ and w 2 are the surfaces of the two openings, we find by a 
treatment, which is given in a more general form in 10, the 
intensity of the rays (polarized in a and of wave lengths be- 
tween A and 7i + d%) which, falling from J^upon opening 1, in 
part, pass to opening 2, 



by dx 

,v , . 

that is 

Of these rays the fraction 1 p goes through the opening 1 
and arrives at the opening 2. 

Tims E- (1-,) T -2tf*- 

If these values of E and A are substituted in the equation 

E I 
A = 
then r = 

Results of the Law 5. 
When any given body a platinum wire for instance is 
gradually heated, it emits, up to a certain temperature, only 
rays whose wave lengths are greater than that of the visible 
rays. At a certain temperature, rays of the wave length of the 
extreme red begin to be visible ; as the temperature rises 
higher and higher, rays of a shorter and shorter wave length 
are added, so that for every temperature, rays of a corresponding 
wave length come into existence, while the intensity of the 
rays of greater wave lengths increase. If the law proven be 
applied to this case, it will be seen that the function / for 
any wave length vanishes for all temperature below that of a 
certain temperature, depending on the wave length for higher 
temperatures increases with the same. From this it follows, 
when the same law is applied to other bodies, that all bodies, 
whose temperature is gradually raised, begin to send out rays 
of the same wave length at the same temperature, and begin to 
glow with red rays at the same temperature, and at a higher 
common temperature, yellow, and so on. The intensity of 
rays of a certain wave length which different bodies send out at 
the same temperatures may, however, be very different ; it is 
proportional to the absorptive powers of bodies for rays of that 
particular wave length. At the same temperature accordingly 
metal glows more brightly than glass, and this more brightly 
than a gas. A body that remains perfectly transparent at the 



highest temperature would never become incandescent. Into 
a ring of platinum wire of about 5mm diameter, I introduced 
some phosphate of soda and heated it in the nonluminous flame 
of the Bunsen burner. The salt melted and formed a fluid 
lens and remained perfectly clear; but it emitted no light, 
while the platinum ring in contact with it radiated the most 
brilliant light. 

Draper 1 has drawn the conclusion from investigations that 
all solid bodies begin to glow at the same temperature. From 
his researches he lias, however, noted that certain bodies like 
chalk, marble, fluor spar glow at a lower temperature than 
they should according to this law; he called this luminosity 
phosphorescence, and said it clearly differed from glowing, by 
the color. But whatever name may be given to this luminos- 
ity, it is in contradiction with law, 3, and a body which shows 
it must therefore not satisfy the assumptions which were made 
in the proof of the law, that, at a constant temperature, it must 
remain unchanged ; phosphorescence is not purely an effect of 
heat, and is not exclusively determined by the temperature, 
but is produced by changes in the body ; if these changes 
whether they are chemical or of another nature have ceased 
then the phosphorescence must vanish. 


From the law, 3, it follows that a body, which absorbs more 
rays from one plane of polarization than from another, sends 
out in the same ratio more rays from the first plane of polar- 
ization than from the second. Consequently, as is known to 
happen, a glowing opaque body having a smooth surface sends 
out light in directions oblique to this surface which is 
partially polarized perpendicularly to the plane passing 
through the ray and the normal to the surface ; of the incident 
rays, which are polarized perpendicularly to the plane of in- 
cidence, the body reflects less, but also absorbs more than it 
does of rays whose plane of polarization is the plane of in- 
cidence. According to this law the state of polarization of the 
rays sent out may easily be given if the law ot the reflection of 
the incident rays is known. 

1 Phil. Mag. XXX. p. 345 ; Berl. Ber. 1847. 



A tourmaline plate, cut parallel to the optic axis, absorbs, 
at ordinary temperatures, moraof the rays which strike it nor- 
mally, if the plane of polarization of these is parallel to the 
axis than when it is perpendicular to it. Assuming that the 
tourmaline plate retains this property when it is at a glowing 
heat, it must give out rays in a direction normal to it, which 
are partially polarized in the plane passing through the optic 
axis and which is the plane perpendicular to that which is 
called the plane of polarization of the tourmaline. 1 have 
proved this striking deduction from theory by experiment and 
it confirmed the same. The tourmaline plates employed with- 
stood a considerable temperature, glowing for a long time in 
the flame of the Bunsen burner without undergoing any per- 
manent change; only after cooling did they appear dull at the 
edges. The property of polarizing transmitted light was 
retained even at an incandescence, although in a considerable 
less degree than at a lower temperature. This appeared on 
observing, through a double refracting prism, a platinum wire 
made incandescent in the flame and placed behind a tourma- 
line plate. The two images of the platinum wire were of un- 
equal brightness, although the difference was much less than 
when the tourmaline plate was outside of the flame. The 
double refracting prism was then given the position in which 
the difference of the intensities of the two images was a maxi- 
mum ; suppose the upper image were the brighter ; then, after 
removal of the platinum wire the two images of the tourmaline 
plate were compared. The upper image was not strikingly, 
but, unmistakably, darkerthan the other; both images appeared 
exactly like to two similar incandescent bodies, of which the 
upper had a less temperature than the lower one. 


Still another result of the law established may, in conclusion, 
be admitted here. When a space is surrounded by bodies of 
the same temperature, and no rays can penetrate through these 
bodies, every pencil in the interior of the space is so consti- 
tuted, with respect to its quality and intensity, as if it pro- 
ceeded from a perfectly black body of the same temperature, 
and is therefore independent of the nature and form of the 



bodies, and only determined by the temperature. The truth 
of this statement is evident if we consider that a pencil of rays, 
which has the same form, but the reverse direction to that 
chosen, is completely absorbed by the infinite number of reflec- 
tions which it successively experiences at the assumed bodies. 
In the interior of an opaque glowing hollow body of given tem- 
perature there is, consequently, always the same brightness 
whatever its nature may be in other respects. 


GUSTAV ROBERT KIRCHHOFE, the son of Counselor-at-law 
Kirchhoff, was born March 12, 1824, at Kdnigsberg. He took 
his degree of doctor of philosophy at the University in 1847. 
The following year he became private-docent at the University 
of Berlin. He early showed those rare mathematical faculties 
which later distinguished him. As early as his eighteenth year 
he decided upon physics as the branch to which he should 
devote his life's work. By 1845 he had investigated electric 
currents, and established the two so-called Kirchhoff's laws for 
current conduction. Other important papers on electricity fol- 
lowed in rapid order. In 1854 he was called to Breslau, where 
he became associated with Bunsen. He went to Heidelberg in 
1854 where Bunsen had preceded him. Here in his prime he 
wrought and sought for twenty years, and in connection with 
Bunsen achieved some of the most important discoveries in the 
history of physical science. In 1875 he accepted, after twice 
declining an invitation to the University, a call to the chair of 
theoretical physics at Berlin where he became associated with 
his former colleague von Helmholtz. Here he delivered for 
eleven years (with serious interruption in the last two years) his 
famous courses of lectures on theoretical physics. It is during 
this period that we find the most brilliant aggregation at Berlin 
of scholars in the faculty of mathematics and physics during 
the century. His contributions extend over optics, heat, fluid, 
motion, electricity, elasticity, etc., and all bear the imprint of 
the great genius he was. He died unexpectedly Oct. 17, 1887, 
after many months of disability. His papers and lectures 
have been collected and edited and now form one of the endur 
ing monuments in physical science. 





Poggendorf ',? A nnalen, Band 1 10, 1 860 ; Gesammelte Abliand- 
lungen von G. Kirclilioff. pp. 598-625, 1882. 




Methods of Purifying Salts 101 

Apparatus described . . . . . . .103 

Sodium . . . . . . . , . . 107 

Lithium . . . 109 

Potassium . . . . . . . . . .113 

Strontium, . . 113 

Calcium . . . . . . . . . .115 

Barium 119 

Advantage of Spectrum Analysis over other Methods . . 122 
Law of Reversed Spectra ... . 123 



IT is well known that many substances have the property 
when they are brought into a flame of producing in the spec- 
trum certain bright lines. We can found on these lines a 
method of qualitative analysis which greatly enlarges the field 
of chemical reactions and leads to the solution of problems 
unsolved heretofore. We shall confine ourselves here only to 
the extension of the method to the detection of the metals of 
the alkalis and the alkali earth and to the illustration of their 
value iii a series of examples. 

The lines referred to show themselves the more plainly, the 
higher the temperature and the weaker the natural illuminating 
power of the flame. The gas lamp 2 described by one of us 
gives a flame of very high temperature and very small luminosity; 
this is consequently especially adapted to investigations on 
those substances characterized by bright lines. 

In Figure 1 the spectra are represented which the flames 
referred to give when the salts, as pure as possible, of potassium, 
sodium, lithium, strontium, calcium, and barium are vaporized 
in it. The solar spectrum is annexed in order to facilitate the 

The potassium compound used for the investigation was 
obtained by heating chlorate of potassium which had been six to 
eight times recrystallized beforehand. 

The chloride of sodium was obtained by combining pure car- 
bonate of sodium and hydrochloric acid and purifying the same 
by repeated crystallization. 

The lithium salt was purified by precipitating fourteen times 
with carbonate of ammonium. 

For the production of the calcium salt a specimen of marble 

1 Kirchhoff and R. Bnnsen, Pogg. Ami. Vol. 110. 1860. 

2 Bunsen, Fogg. Ann. Vol. 100 p. 85. 


I 1 & & S % M 


as pure as possible, and dissolved in hydrochloric acid, was 
used. From this solution the carbonate of calcium was thrown 
down by a fractional precipitation with carbonate of ammonium 
in two portions, of which only the latter, precipitated in calcium 
nitrate, was used. The calcium salt thus obtained we dissolved 
several times in absolute alcohol and converted it finally into 
the chloride by evaporating the alcohol and by precipitation 
with carbonate of ammonium in hydrochloric acid. 

In order to obtain the pure chloride of barium we extracted it 
from the commercial salt by pulverizing and boiling repeatedly 
in nearly absolute alcohol. The residue thus extracted and 
freed from alcohol was dissolved in water and thrown down by 
fractional precipitation in two portions, only the second being 
dissolved in hydrochloric acid, and the barium chloride thus 
obtained being further purified by repeated crystallizations. 

In order to obtain chloride of strontium, as pure as possible, 
the commercial salt was crystallized out from alcohol, and frac- 
tionally precipitated in two portions with carbonate of ammon- 
ium, the second part being dissolved in nitric acid and the ni- 
trate freed from the last traces of calcium by pulverizing and 
boiling with alcohol. From the product thus purified the chlo- 
ride of strontium was obtained finally by precipitating with 
carbonate of ammonium and dissolving the precipitate in 
hydrochloric acid. All these purifications were made in plat- 
inum vessels as far as it was possible. 

Figure 2 represents the apparatus which we have used 

mainly in the observation 
of the spectra. A is a 
box blackened on the in- 
side the bottom of which 
has the form of a trapez- 
ium and rests on three 
feet ; the two inclined 
sides of the same form an 

FIG 2 angle with one another of 

about 58 and carry the 

two small telescopes B and C. The ocular of the first is removed 
and replaced by a plate in which is a slit formed of two brass 
cheeks which are placed at the focus of the objective. The 



lamp D is so placed before the slit that the mantle of the frame 
is intersected by the axis of the tube B. Somewhat beneath 
the point where the axis meets the mantle the end of a very fine 
platinum wire bent into a small hook and carried by the holder 
E passes into the same; on this hook is melted a globule of the 
chloride previously dried. Between the objective of the tele- 
scopes B and C is placed a hollow prism F with a reflecting 
angle of 60 and filled with carbon disulphide. The prism 
rests on a brass plate which can be rotated on a vertical axis. 
This axis carries on its lower end the mirror G and above it 
the arm //which serves as the handle to rotate the prism and 
the mirror. A small telescope is adjusted before the mirror 
which gives an image of a horizontal scale placed at a short dis- 
tance. By rotating the prism we can cause to pass before the 
vertical thread of the telescope C the entire spectrum of the 
flame and bring every portion of the spectrum into coincidence 
with this thread. To every reading made on the scale there 
corresponds a particular portion of the spectrum. If the spec- 
trum is very weak the cross hair of the telescope C is illumi- 
nated by means of a lens which throws some of the rays from a 
lamp through a small opening which is placed laterally in the 
ocular of the telescope C. 

The spectra in Fig. 1. obtained by means of the pure chlo- 
ride above mentioned we have compared with those which we 
obtained if we introduce the bromides, iodides, hyd rated oxides, 
sulphates, and carbonates of the several metals into the follow- 
ing flames: 

into the flame of sulphur, 

" " " " carbon disulphide, 

" " " " aqueous alcohol, 

" " non-luminous flame of coal gas, 

" " flame of carbonic oxide, 

" " " " hydrogen and 

" " oxyhydrogen flame. 

From these comprehensive and lengthy investigations whose 
details we may be permitted to omit, it appears that the dif- 
ference in the combinations in which the metals were used, the 
multiplicity of the chemical processes in the several flames, and 
the enormous differences of temperatures of the latter exert no 
influence on the position of the spectral lines corresponding to the 
individual metals. 



How considerable the differences of temperature mentioned 
are, is shown by the following treatment. 

We may arrive at an approximation of temperature of a 

flame by means of the equation t = -?~, in which t is the 

temperature of the flame sought, g the weight of the substance 
burning in oxygen, w the heat of combustion of the same, p the 
weight and s the specific heat of one of the products of combus- 

If we take as the heat of combustion 

of sulphur as 2240 C 



' carbon disulphide 

' hydrogen 

' marsh gas 

' elayle 

* ditetryle 

' carbonic oxide 

and place according to Regnault the specific heat at constant 


for sulphurous acid =0. 1553 

" carbonic acid =0.2164 

" nitrogen =0.2440 

" aqueous vapor =0.4750 

we find accordingly the temperature 

of the sulphur flame 1820 C 

' bisulphide of carbon flame.... 2195 

' coal gas flame 1 2350 

' carbonic oxide flame 2 3042 

' hydrogen flame in air 3 3259 

' oxyhydrogen flame 4 8061. 

It appears that the same metal compound gives in one of 
these flames a spectrum as much more intense as the tempera- 
ture is higher. Of the compounds of these metals, those give 
the greatest intensity in a flame which have the greatest 

In order to obtain a further proof that each of the severally 
mentioned metals always give the same bright lines in the 
spectrum, we have compared the spectra referred to with those 

1 Liebig's Ann. Vol. CXI. p. 258 

8 Gasometric Methods by R. Bunsen. p. 254. 

3 Ibid. 

4 Ibid. 



which an electric spark produces which passes between 
electrodes made from these metals. 

Small pieces of potassium, sodium, lithium, strontium, and 
calcium were fastened on a fine platinum wire and so melted in 
pairs within glass tubes that they were separated by a distance 
of 1 to 2mm from one another the wires piercing the sides of 
the tubes. Each of these tubes was placed before the slit of 
the spectroscope ; by means of a Bnhmkorff's induction 
apparatus, we caused electric sparks to pass between the metal 
pieces mentioned and compared the spectrum of the same with 
the spectrum of a gas flame in which the chloride of the cor- 
responding metal was brought. The flame was placed behind 
the glass tube. When the Ruhmkorff apparatus was thrown 
alternately in and out of action it was easy to be convinced, 
without any accurate measurement, that, in the brilliant spec- 
trum of the spark, the bright lines of thespectrnmof the flame 
were present undisplaced. In addition to these there appeared 
other bright lines in the spark spectrum a part of which must 
be attributed to the presence of foreign metals in the electrodes, 
others to nitrogen which filled the tubes after the oxygen had 
partly oxidized the electrodes. 1 

It appears, accordingly, beyond a question that the bright 
lines of the spectra indicated maybe considered as certain proof 
of the presence of the metal in consideration. They can serve 
as reactions by means of which this material may be detected 
more certainly, and quickly and in smaller quantities than by 
any other analytical method. 

The spectra, represented, refer to the case when the slit is 
wide enough so that only the most prominent of the dark lines 
of the solar spectrum are visible, the magnifying power of the 
observing telescope being small (about four-fold) and the 
intensity of the light moderate. These conditions seem to us 

1 In one investigation with strontium electrodes we used a tube filled 
with hydrogen instead of nitrogen, and the stream of sparks was trans- 
formed very soon into an arc, while the sides of the tuhe were covered 
with a gray precipitate. On opening the tube nnder rock-oil it appeared 
that the hydrogen had vanished and a vacuum existed. The gns 
appears, therefore, at the enormous temperature of the electric spark, to 
have dissociated the strontium oxide which had not been completely 
removed from the surface of the metal. 



most advantageous when it is necessary to carry out a chemical 
analysis by spectral observations. The appearance of the 
spectrum may under other conditions be quite different. If the 
purity of the spectrum is increased, many of the lines appearing 
as single, resolve themselves into several, the sodium line, for 
example, into two ; if the intensity is increased new lines appear 
in many of the spectra shown and the relation of the brightness 
of the old ones becomes different. In general the brightness of 
a darker line increases with greater luminosity more rapidly 
than the brighter ones,but not so much that the former exceed 
these. A clear example of this is given by the two lithium 
lines. We have observed only one exception to this rule, 
namely, with the line Ba ?, which, with low luminosity, is 
barely visible while Zto^appears very distinct, and, with greater 
luminosity, much brighter than the former. This fact appears 
of importance, and we shall make a further study of the same. 
We will now consider more closely the characteristics of the 
several spectra, the knowledge of which is of importance from 
a practical standpoint, and indicate the advantage which the 
chemical analytical method founded upon it furnishes. 


Of all the spectral reactions that of sodium is the most sen- 
sitive. The yellow line Na a, the only one which is shown in 
the sodium spectrum coincides with Fraunhofer's line D and is 
characterized by its peculiarly sharp boundary and its extraor- 
dinary brilliancy. If the temperature of the flame is very high 
and the quantity of the substance used very great, traces of a 
continuous spectrum are seen in the immediate neighborhood 
of the line. Lines of other substances, in themselves very 
weak, lying near it appear still weak and will, therefore, often 
first be visible after the sodium reaction has begun to disappear. 

In the oxygen, chlorine, iodine and bromine compounds in 
sulphuric acid and carbonic acid the reaction is most evident. 
But it is present also in the silicates, borates, phosphates and 
other non -volatile salts. 

Swani has already called attention to the minuteness ef the 

1 Pogg. Arm. Vol. C, p. 311. 



quantity of common salt which can produce the sodium line 

The following investigation shows that chemistry produces 
no single reaction which in the remotest degree can compare in 
sensitiveness with this analytical spectral determination of 
sodium. We detonized in one corner of the experiment room 
which contained about 60 cubic meters of air and as far as 
possible from our apparatus three milligrams of chlorate of 
sodium with milk sugar while the non-luminous flame was 
observed before the slit. After some minutes, the flame, becom- 
ing gradually colored pale yellow, gave a strong sodium line, 
which, after ten minutes, again completely vanished. From the 
weight of the detonized salt and the air contained in the room 
it is easy to calculate that in a unit weight of the latter not a 
?oWr<rzrr>kh part of sodium smoke could have been suspended. 
As the reaction can be readily observed in a second, and as, in 
this time, according to the rate of flow and the composition 
of the gases in the flame, onty about 50 ccm or 0.0647 grams of 
air which contained less than ^otfoWoirth of sodium salt, reach 
the state of incandescence in the flame, it follows that the eye 
is capable of detecting less than ^ootrotfth f a milligram of 
sodium salt with the greatest distinctness. With such a sen- 
sibility of the reaction it is evident that only rarely is a sodium 
reaction not visible in glowing atmospheric air. The earth is 
covered over more than two-thirds of its surface with a solu- 
tion of chloride of sodium, which, by the waves breaking into 
foam, is transformed continually into spray; the particles of 
sea-water, which reach the atmosphere in this way, evaporate 
and leave behind them motes of salt which vary in magnitude, 
but, as it appears, are rarely absent from the atmosphere, and, 
perhaps, serve to supply the small organisms the salt which the 
larger plants and animals secure from the ground. The 
presence in the air of salt, easily shown by spectral analysis, is 
yet of interest from another standpoint. If, as we yet can 
scarcely doubt, there are catalytic influences which are the 
cause of the miasmic spread of disease, it is possible that an 
antiseptic substance, such as salt, even in vanishingly small 
quantities, may indeed not be without definite influence upon 
such processes in the air. From daily and long continued 



spectrum observation it would be easy to learn whether the 
variation in the intensity of the spectral line Ncta, produced by 
the sodium combination in the air, is related in any degree to 
the appearance and the spread of endemic diseases. 

In the exceedingly delicate sodium reaction may also be 
sought the reason why all bodies exposed to the air show the 
sodium line after a time when heated in the flame, and why it 
is possible with only a few compounds to eliminate the last 
trace of the sodium line No, a by crystallizing it out ten or more 
times from water which has come in contact with platinum 
vessels only. A hair wire of platinum, which has been freed, 
by heating, from every trace of sodium, shows the reaction 
most vividly again, if it is exposed some hours to the air. Dust 
which settles in the room from the air shows it in the same 
degree, so that, for example, the slapping of a dusty book is 
quite sufficient to produce at a distance of several spaces the 
most brilliant flashes of the No, a line. 


The incandescent vapors of the lithium compound give two 
sharply defined lines, one a very weak yellow Li (3 and a red 
brilliant line Li a. In certainty and delicacy this reaction ex- 
ceeds all those known heretofore in analytical chemistry. It 
approximates in sensibility that of the sodium reaction perhaps 
because the eye is more sensitive for yellow rays than for re'd. On 
detonizing nine milligrams of carbonate of lithium with a large 
excess of milk sugar and potassium chlorate in the room which 
contained about 60 cubic meters of air, the line became quite 
evident. The eye can therefore in this way, as a calculation 
similar to the one made above will show, perceive less than 
T _j TFTTTT th of a milligram of carbonate of lithium with the 
greatest distinctness. 0.05 grams of the same salt, detonized in 
the way already mentioned, made it possible to observe the Li a 
line in the air of the same room during more than an hour. 

The oxygen, chlorine, iodine and bromine compounds are 
most suitable for observing lithium. But the carbonate, sul- 
phate, and even phosphate are almost as well suited for this 
purpose. Minerals containing lithium, as triphyllin, triphan, 
petalit, lepidolith, need only to be held in the flame in order 



to give the line Li a with an intense lustre. In this way it is 
possible to show the presence of lithium in many f eld -spars, 
for example in orthoclase from Baveno. The line is seen only 
momentarily immediately after the insertion of the specimen in 
the flame. Thus mica from Altenberg and Penig indicates the 
presence of lithium while on the contrary mica from Miask, 
Ashaffenburg, Modum, Bengal, Pennsylvania, etc., is free from 
lithium. When in naturally deposited silicates only a vanish- 
ingly small quantity of lithium is present, it escapes immediate 
observation. The test in such cases is then best made in the 
following way: we digest and evaporate a small quantity of the 
substance for examination with hydrofluoric acid or fluoride of 
ammonium, moisten the remainder with sulphuric acid, and 
dissolve the dry mass with absolute alcohol. The alcoholic 
solution is then evaporated to dryness, again dissolved with 
alcohol, and the fluid, thus obtained, evaporated in as shallow a 
dish as possible. The product which remains can be easily 
scraped together by means of an erasing knife and brought into 
the flame on platinum wire, i^th of a milligram of the same is 
usually quite sufficient for the experiment. Other compounds 
than the silicates, in which we may wish to detect the least 
traces of lithium, maybe transformed into sulphates by evapo- 
ration with sulphuric acid or in any other way and then treated 
as above. 

By means of these experiments, the unanticipated conclusion 
is readily drawn that lithium belongs to those substances which 
are most widely distributed in nature. This is easily shown by 
means of 40 cubic centimeters of sea-water which was collected 
in the Atlantic ocean in latitude 41 41' and longitude 39 14'. 
Ashes of Fucoids (kelp) which was driven on to the Scottish 
coast from the Gulf Stream contained appreciable traces of it. 
All orthoclase and quartz from the granite of the Oldenwald 
which we have tested show a lithium content. A very pure 
drinking water from a spring on the western granitic declivity 
of the Neckar valley in Schlierbach near Heidelberg contained 
lithium, while the spring rising in the red sandstone which 
supplies the water pipes of this chemical laboratory was free 
from it. Mineral water, in a litre of which lithium can 
scarcely be detected by the ordinary analytical methods, shows 



the Li a line frequently if we put a drop of the same into the 
flame on a platinum wire. 1 All the ashes of woods in the Olden- 
wald which grow on granite soil, as well as Russian and 
other commercial potashes examined by us, contain lithium. 
Neither, even, in the ashes of tobacco, vine leaves, vine-wood 
and grapes,' 2 as well as in the ashes of crops which were culti- 
vated in the Rhine plain near Waghausel, Deidesheim and 
Heidelberg on non-granitic earth, was lithium lacking, nor in 
the milk of the animals which were fed upon these crops. 3 

It will be scarcely necessary to remark that a mixture of 
volatile sodium and lithium salts shows, along with the reaction 
of sodium, that of lithium with a scarcely less preceptible sharp- 
ness and distinctness. The red line of the last appears still 
quite distinct when a small bead containing the y^^th part of 
lithium salts is introduced into the flame, where the eye, 
unaided, perceives in the same, nothing more than yellow 
light of sodium without any indication of red coloration. On 
account of the greater volatility of lithium salts, the sodium 
reaction lasts somewhat longer. When, therefore, it is desired 
to detect very small traces of lithium along with sodium, the 
bead for testing must be introduced into the flame whilst we 
are observing through the telescope. We then often observe 
the lithium line only for a few moments during the first 
products of volatilization. 

In the production of lithium compounds on a commercial 
scale spectrum analysis is a means of inestimable value in the 
selection of the raw material used and the determination of an 
efficient method of manufacture. Thus for example, it is only 
necessary to evaporate a drop of the different mother-liquors in 

1 When it is required to introduce a liquid into the flame we bend in 
the end of a horse-hair platinum wire, a ring of suitable diameter and 
hammer the same flat. If we let a drop of the fluid fall into the ring 
thus formed a sufficient quantity for the investigation remains hanging 

2 Lithium is concentrated so much in the mother-liquors in the man- 
ufacture of tartaric acid that we can obtain considerable quantities from 

3 Dr. Folwarcznyhas even been able to show with the lithium line Li a 
the lithium compounds in the ash of human blood and of muscular 



the flame and observe through the telescope, in order to show 
at once, that, in many of these saline residues, a rich and 
hitherto overlooked lithium source exists. Thus in the process 
of preparation, we can follow any loss of lithium in the as- 
sociated products and wastes by means of the spectral reaction, 
and thus easily seek more efficient methods of production than 
those heretofore used. 1 


The volatile potassium compounds produce in the flame a 
very extended continuous spectrum which only show two 
characteristic lines ; the first K a, in the outermost red border- 
ing on the ultra red rays falls exactly on the dark line A of the 
solar spectrum; the second K $ far in the violet toward the 
other end of the spectrum, corresponds likewise to a Fraunhofer's 
line. A very weak line, coinciding with the Fraunhofer's line 
B, which, however, is only visible with an intense flame, is less 
characteristic. The blue line is somewhat weak but is almost as 
well suited for detecting potassium as the red line. The position 
of both lines, in the neighborhood of the limits of the rays per- 
ceptible by the eye, renders the reaction somewhat less sensitive. 

In the air of our room it became first visible when we burned 
about one gram of chlorate of potassium mixed with milk 
sugar. We can, therefore, make clear to the eye in this way 
about -nnr^h of a milligram of chlorate of potassium. 

Potassium hydrate and all compounds of potassium with 
volatile acids, show the reaction without exception. Potassium 
silicate and similar non-volatile salts, on the contrary, produce 
it only when the potassium is present in large quantities. 
With small amounts, the test bead may be melted together 
with some carbonate of sodium in order to make the char- 
acteristic lines visible. The presence of the sodium does not 
prevent the reaction and hardly affects the sensibility. Ortho- 

1 We obtained by such an approved method from two jars of mineral 
water (about four litres) a mother-water, which gave on evaporation 
with sulphuric acid a residue of 1.2 K, half an ounce of carbonate of 
lithium of the purity of the commercial, whose cost would be about 
140 fl. per pound. A great number of other mother-waters which we 
examined showed a like wealth iu lithium compounds. 



clase, sanidine, and adularia may easily be distinguished in 
this way from albite, oligoclase, Labradorite, and anorthite. 
In order to detect traces of potassium, vaiiishingly small, we 
need to heat to a feeble incandescence the silicate, with a large 
excess of fluoride of ammonium, in a platinum crucible and in- 
troduce the residue into the flame on a platinum wire. In this 
way we find that almost every silicate contains potassium. 
The lithium salts disturb the reaction but little. Thus, for 
example, it is only necessary to hold the ash end of a cigar in 
the flame before the slit, in order to produce at once very dis- 
tinctly the yellow line of the sodium and the two red ones of 
potassium and lithium, the last metal being scarcely ever 
absent in tobacco ash. 


The spectra of the alkali earths are not so simple as those of 
the alkalis. That of strontium is characterized, particularly, by 
the absence of green bands. Eight lines of the same are quite re- 
markable namely six red, one orange and one blue. The orange 
line Sr a which appears close to the sodium line toward the red, 
the two red lines Srp, Sr y and finally the blue line Sr 6 are the 
most important in their position and intensity. In order to 
test the sensibility of the reaction we heated quickly in a plat- 
inum dish, over a large flame, an aqueous solution of chloride 
of strontium of known concentration until the water was 
evaporated and the dish began to glow. The salt then began to 
decrepitate into microscopic particles which were thrown into 
the air in the form of white smoke. A weighing of the salt 
residue in the dish showed that in this way 0.077 grams of 
chloride of strontium had passed out into the 77,000 grams' 
weight of air of the room in form of a fine dust. After the air 
of the room had been thoroughly mixed, by means of an open 
umbrella moved rapidly about, the characteristic lines of the 
strontium spectrum were very beautifully outlined. We can ac- 
cording to this experiment estimate the amount of chloride of 
strontium preceptible at T WW fcn f a milligram. 

The chlorine and the other haloid compounds of strontium 
give the most distinct reaction. Strontium hydrate and carbon- 
ate of strontium show them much more feebly; the sulphate 



still less distinctly; the compounds, with the non-volatile 
acids, the weakest or not at all. We must therefore introduce 
into the flame, first, the bead for testing by itself, and then 
again, after previously moistening with hydrochloric acid. If 
we assume sulphuric acid in the bead, we must hold it some 
moments in the reducing part of the flame before moistening 
with hydrochloric acid, in order to transform the sulphate into 
the sulphide which is decomposed by hydrochloric acid. To 
detect strontium in compounds of silicic, phosphoric, boracic 
or other non-volatile acids we proceed best in the following 
manner: for fusing with carbonate of sodium a conical spiral 
of platinum wire is used instead of a platinum crucible. The 
same is made white hot in the flame and dipped into dry fine 
pulverized carbonate of sodium which, when possible, contains 
enough water so that the necessary quantity of the salt remains 
hanging to the same on the first immersion. Fusion can be 
effected in this spiral much quicker than in the platinum 
crucible, since the mass of the platinum heated is small and 
the salt to be fused comes into immediate contact with the 
flame. If we transform the fine pulverized substance to be 
tested into the glowing fluid soda by means of a small plat- 
inum spatula, and maintain it in a glowing state for a few 
minutes, we need only to knock the spiral, inverted with its 
vertex upward, on the edge of the lamp stand in order to 
obtain the contents of the same in the form of a large solidified 
bead. Wo then cover the bead with a sheet of writing paper 
and press it by means of an elastic knife blade, which we also 
use after removing the paper, in order to reduce the mass still 
farther to the finest powder. This is collected on the edge of 
a plate slightly tilted and carefully covered with hot water 
which is allowed to flow backwards and forwards over the sub- 
stance, heaped up by gentle tipping of the plate and finally, 
the fluid, remaining over the sediment, is decanted. It is easy, 
by repeated heating of the plate, to draw off the soluble salt 
after several repetitions of this process without stirring up the 
sediment and losing an appreciable amount of the same. If 
instead of water we use a common salt solution, the operation 
may be conducted more quickly and certainly. The residue 
contains the strontium as carbonate, of which a few tenths of a 



milligram, moistened with a little hydrochloric acid on a plat- 
inum wire, give a brilliant reaction. In this way, without 
platinum crucible, mortar, evaporating dish, and without 
funnel and filter, it is possible to carry out, in a few minutes, 
all the necessary operations of fusing, powdering, digesting 
and washing. 

The reaction of potassium and sodium is not affected by the 
presence of strontium. The lithium reaction takes place along 
with the three mentioned with perfect distinctness, if the 
quantity of lithium is not too small with respect to that of the 
strontium. The lithium line Li a then appears as a narrow in- 
tensely red and sharply defined band upon the weaker red 
background of the broad strontium band Sr p. 


The spectrum of calcium can be immediately distinguished at 
the first observation from the four spectra already considered 
in that a very characteristic and intense line Ca ft is present in 
the green. Also a second not less characteristic feature is the 
very brilliant orange line Ca a which lies considerably farther 
toward the red end of the spectrum than the sodium line Naa 
and the orange line of strontium Sr a. By burning a mixture 
of calcium chloride, chlorate of potassium and milk sugar we 
obtain a smoke whose reaction is approximately of the same 
sensibility as that of the fumes from the chloride of strontium 
under the same conditions. It follows from an examination 
made in this way that T <yo 6 (nnj- of a milligram of calcium chlo- 
ride can be detected easily and with absolute certainty. Only 
the calcium compounds, volatilized in the flame, show this re- 
action, and the more volatile they are the more distinct it is. 
Chloride of calcium, iodide of calcium, and bromide of calcium 
are best in this respect. Sulphate of calcium gives a spectrum 
only after it has become basic but then very brilliantly and 
long continued. In the same way the reaction of the carbonate 
becomes distinct after the acid has been driven off. 

Compounds of calcium with non-volatile acids remain indif- 
ferent in the flame, but if they are attacked by hydrochloric 
acid, the reaction may be easily obtained in the following way: 



we introduce a few milligrams, or perhaps only a few tenths of 
a milligram, of the finely pulverized substance on the flat plat- 
inum ring, somewhat moistened, into the less heated portion of 
the flame until the powder is frittered without being melted. 
If we allow a drop of hydrochloric acid to fall on the ring the 
greater part of it will remain hanging. If we pass this drop 
before the slit of the spectroscope into the hottest part of the 
flame it volatilizes without boiling on account of its spheroidal 
condition. If during the volatilizing of the drop we look into 
the telescope there appears at the instant when the last portion 
of the fluid has been evaporated a brilliant calcium spectrum- 
which flashes out but for a moment with a small amount, but 
continues a longer or a shorter time with considerable quan- 
tities of metal. 

Only in silicates which are attacked by hydrochloric acid can 
the calcium be found in this way; in silicates which are not 
attacked by hydrochloric acid the test is best obtained in the 
following way: a few milligrams of the substance to be tested 
are pulverized as fine as possible and placed on a flat platinum 
crucible cover with about a gram of half-dissolved fluoride of 
ammonium and the cover held in the flame until it volatilizes 
the fluoride of ammonium. We moisten the salt residue re- 
maining on the cover with one to two drops of sulphuric acid, 
and drive off the excess of the same by gently heating over the 
flame. If the residue of the sulphates now remaining on the 
cover be scraped together with the finger-nail or a spatula and 
about a milligram of the same be introduced into the flame by 
means of a wire, we obtain, if K 9 Na and Li are present, the 
characteristic reaction of these three bodies simultaneous or 
successively. If calcium and strontium be also present their 
spectra usually first appear after K, Na and Li have been 
vaporized. The reaction of these metals fails with weak con- 
tents of calcium and strontium; we obtain it, however, imme- 
diately if we introduce the wire for a few moments into the 
reducing part of the flame, moisten it with hydrochloric acid, 
and bring it again into the flame. 

All these tests, as the heating of it alone, or with hydro- 
chloric acid, the treatment with ammonium fluoride alone, or 
with sulphuric and hydrochloric acid, provide the mineralogist 



and still more the geologist with a series of highly simple tests 
for determining many substances occurring in nature even in 
the smallest particle, such, for example, as the minerals so 
similar to one another, consisting of double silicates, contain- 
ing lime, with a certainty which is scarcely attainable with an 
abundant supply of material by means of an extended and pro- 
tracted analysis. Some examples will illustrate this best. 

1. A drop of sea-water evaporated on a platinum wire showed 
a strong sodium reaction, and after volatilizing the chloride of 
sodium a weak calcium reaction which, by moistening the wire 
with hydrochloric acid, became for a moment very brilliant. 
If we treat a few decigrams of the residue of sea-water, in the 
way described for lithium, with sulphuric acid and alcohol we 
easily obtain the reaction of potassium and lithium. The pres- 
ence of strontium in sea- water can be observed best in the 
boiler crusts of steamships. The filtered hydrochloric acid 
solution of the same leaves, on evaporation and solution in the 
smallest quantity of alcohol, a dull yellow coloring from the 
basic iron salt which is deposited after some days and collected 
on a filter and washed with alcohol. The filter burnt on a fine 
platinum wire gives, along with the calcium line, a complete 
and bright strontium spectrum. 

2. Mineral waters often show at once the potassium, sodium, 
lithium, calcium, and strontium reactions. For example, if 
we introduce a drop of Durkheim or Krauznach mineral water 
into the flame we obtained the lines Na a, Li a, Ca a, and Ca /?. If 
we use instead of the mineral water a drop of the mother liquid 
the same lines appear with great brilliancy. In proportion as 
the chloride of sodium and lithium are volatilized and the 
chloride of calcium has become more basic, the characteristic 
lines of the strontium spectrum gradually develop themselves 
and, becoming brighter, finally are seen in all their extent. We 
obtain here also, by a mere glance at a single drop vaporized in 
the flame, the complete analysis of the mixture of five sub- 
stances in a few moments. 

3. The ash of a cigar moistened with some HC1 and held in 
the flame gives the lines Naa, Ka, Li a, Caa, Cap. 

4. Potash glass of a combustion tube gave, both with and 
without hydrochloric acid, Na a and K a, and treated with 



fluoride of ammonium and sulphuric acid Caa, Cap and traces 
of Li a. 

5. Orthoclase from Baveno gives either alone or with hydro- 
chloric acid only No, a. with traces of K a and Lia\ with fluoride 
of ammonium and sulphuric acid the intense line Naa, K a and 
somewhat less distant Li a. After volatilizing the constituents 
thus observed the bead introduced, into the flame with HCl, 
gives only a scarcely distinguishable flash of the lines Caa arid 
Cap. The residue remaining on the platinum wire after this 
test showed, when moistened with cobalt solution and heated, 
the characteristic color of alumina. If we employ the well- 
known reaction of silicic acid also it follows from this examina- 
tion, made in a few minutes, that the orthoclase from Baveno 
contains silicic, alumina, potash with traces of soda, lime and 
lithia whilst every trace of baryta and strontia fail. 

6. Adularia from the Gotthard conducted itself quite similar 
to the orthoclase from Baveno only that the lithium reaction 
fulled entirely and the calcium reaction nearly so. 

7. Labradorite from St. Paul gives, by itself, only the sodium 
line Na a and not the calcium spectrum. But the sample moist- 
ened with hydrochloric acid gives the calcium lines CWand 
Cap very brilliantly. With the test by means of fluoride of 
ammonium we still obtain a weak potassium reaction and very 
faint traces of lithium. 

8. Labradorite from the Diorite of Corsica comported itself 
similarly only that the traces of the lithium reaction were 

9. Mosanderite from Brevig and Tscheffkinite from thellmen 
mountains gave by itself only the sodium reaction, but the cal- 
cium line Caa and Cap when treated with hydrochloric acid. 

10. Melinophane from Lamoe gave by itself only Naa but 
with hydrochloric acid Caa, Cap and Li a. 

11. Scheelite and Sphene gave, on treatment with hydro- 
chloric acid, the very brilliant calcium reaction. 

12. If small quantities of strontium are present with calcium 
we employ the line Sr6 most advantageously to detect the for- 
mer. By means of the same it is easy to detect a small content 
of strontium in very many sedimentary limestones. Na a,Li a 
R a particularly Li a are shown immediately on heating the 



limestone in the flame. Those minerals, converted into cal- 
cium chloride by hydrochloric acid and introduced into the 
flame in this form, give the same lines and besides frequently 
the line Sr 6 quite distinctly. But this appears only for a short 
time and most distinctly whilst it is being developed in the 
course of the volatilization in the flame and shortly before the 
fading out of the calcium spectrum. 

In this way the lines Naa, Li a, Ka,Caa,Cap, Sr 6 were found 
in the following limestones : 

Silurian limestone 1 from Kugelbad near Prague, 

Shell limestone from Rohrbach near Heidelberg, 

Lias limestone from Malsch in Baden, 

Chalk from England. 

The following limestones showed the lines Naa, Lia, Ka,Ca a , 
Cap, without the blue strontium line: 

Marble from the granite of Auerbach, 2 

Devonian limestone from Gevolstein in the Eifel, 

Carboniferous limestone from Planite in Saxony, 

Dolimite from Nordhausen in the Hartz, 

Jura limestones from the Streitberg in Franconia. 

We now see from these few experiments that extended and 
careful spectral analysis of the lithium, potassium, sodium, 
and strontium content of various limestone formations are of 
the greatest geological interest with respect to their order of 
formation and their local disposition and may possibly lead to 
unexpected conclusions on the nature of the earlier ocean and 
sea basins in which the formation of these minerals took place. 


The spectrum of barium is the most complicated of the 
spectra of the alkalis and alkaline earths. It is distin- 
guished at the first glance from those heretofore examined by 

1 The lithium line could not be detected with certainty in this class of 
minerals, the line Sr <5 on the contrary was very strong. 

2 By means of the experiment with alcohol above described enough 
nitrate of strontium was obtained from twenty grams of marble to pro- 
duce a bright and complete spectrum of strontium. Whether the re- 
maining limestones treated in this way show a strontium content we 
have not investigated. 



the green lines Ba a and Bap, which exceed all the others in 
brilliancy, appearing first and disappearing last in weak reac- 
tions. Ba y is less distinct but is still always to be treated as a 
characteristic line. The relatively great extension of its spec- 
trum is the reason why the spectral reaction of the barium com- 
pounds is somewhat less delicate than those of the substances 
heretofore examined. 0.3 grams of chlorate of barium 
burned in onr room with milk sugar gave, after the air had 
been thoroughly mixed by moving an open umbrella, the line 
Ba a most distinctly, for a long time. We may therefore con- 
clude from a calculation made similar to that for sodium, that 
the reaction will show, with perfect distinctness, not less than 
TTJ ^oth of a milligram. 

Chloride, bromide, iodide, and fluoride of barium, the hy- 
drated oxide, the sulphate, and the carbonate, give the reac- 
tion most markedly and can therefore be determined by 
immediate heating in the flame. 

Silicates decomposable by hydrochloric acid containing ba- 
rium give the reaction, if, as indicated in the case of lime, they 
are introduced into the flame with, a drop of hydrochloric acid. 
Thus, for example, barytharmotome treated in this way gives 
the line Caa Cap along with the lines Baa.Bap. 

Compounds of barium with non-volatile acids, which are 
indifferent with or without hydrochloric acid in the flame, we 
may fuse best, in the way given for strontium, with carbonate of 
sodium and then test the carbonate of barium thus obtained. If 
in such compounds Ca, Ba and Sr occur together in very unequal 
amounts, we dissolve in a drop of sulphuric acid the carbonates 
obtained by fusion and extract the salt with alcohol from the 
evaporated residue. The residue then contains only barium and 
strontium both of which may be easily detected if they do 
not occur in too unequal quantities. When it is desired to test 
for the smallest traces of Sr or Ba, we transform the residue, 
by heating with sal ammoniac, into chlorides, from which the 
chloride of strontium can be easily extracted in a sufficiently 
concentrated state for detection by means of alcohol. If neither 
of the substances to be tested is present in very small quantities 
all such methods of separation are quite unnecessary, as the 
following experiment shows: a mixture of sodium, potassium, 



lithium, calcium, strontium, and barium chlorides which con- 
tained iUh of a milligram of each of these six substances at the 
most, was introduced into the flame and observed. At first 
the brilliant sodium line Naa appeared on the background of 
a weak continuous spectrum. As soon as this began to fade 
away, the sharply defined brilliant red line of lithium Li a ap- 
peared and on the same side of the sodium line, still farther 
away, the faint potassium line Ka whilst the barium lines Baa 
and Ba p appeared very distinctly in their characteristic position 
and peculiar shade. Whilst the compounds of potassium, 
lithium, and barium were slowly volatilized their lines faded 
away, or vanished again gradually in succession until, after a 
few minutes, the lines Caa Cap and Sra /bV/s Sr% Sr 6 became 
visible out of the less and less prominent lines of strontium, as 
from a dissolving view, in all their characteristic form, shade 
and position, and then faded away and entirely vanished after 
a very long time. 

The absence of any one or more of these components could 
be instantly detected, in the observation, by the absence of the 
corresponding lines. 

For those who have become familiar with the individual 
spectra by repeated observation, an accurate measurement of 
the individual lines is unnecessary; their color, their relative 
position, their characteristic definition and shade, the grada- 
tion in their brilliancy, are criterions which are quite sufficient 
for definite recognition even for the inexperienced. These 
characteristics may be compared with the distinguishing fea- 
tures which the various precipitates present in their outward 
appearance, which we use as a reaction test. Just as the char- 
acter of a precipitate determines whether it be gelatinous, pul- 
verulent, flocculent, granular or crystalline, so also the spectral 
lines indicate their characteristics in the sharpness of their 
edges, in the shading off uniformly or irregularly on one or both 
sides, or in their broader or narrower appearance, as the case 
may be. And just as we use only those precipitates in analysis 
which can be produced by the greatest possible dilution, so we 
also use in spectrum analysis for this purpose only those lines 
which require for their production the smallest amount of the 



substance and only a moderately high temperature. In such 
characteristics therefore the two methods are quite similar. 
On the contrary spectrum analysis furnishes, in the color phe- 
nomena used in the reaction, a property which gives it unlimited 
advantage over every other method of analysis. Most of the 
precipitates which are used for the detection of substances are 
white and only a few colored. Further the tint of the latter is 
not very constant and considerably differentiated according to 
the greater or less condensed state of the precipitate. Often 
the smallest mixture of a foreign substance is sufficient to oblit- 
erate completely a characteristic color. Small differences of 
color of the precipitate can therefore be no longer used as a 
chemical test. In spectrum analysis, on the contrary, the colored 
bands remain undisturbed by such foreign influences and are 
undisturbed by the presence of other bodies. The positions 
which they have in the spectrum determine a chemical charac- 
teristic which is of as unalterable and fundamental a nature as 
the atomic weight of the substance, and therefore, permits us 
to determine it with an almost astronomical exactness. What, 
however, gives to the spectral analytical method a peculiar im- 
portance, is the fact that it almost infinitely exceeds the limits 
to which chemical analysis of matter has heretofore reached. 
It predicts for us the most valuable conclusions on the distribu- 
tion and arrangement of geological substances in their forma- 
tion. Already the few investigations, which this memoir 
contains, lead to the unexpected conclusion that not only 
potassium and sodium but also lithium and strontium must be 
counted among the substances of the earth most widely scat- 
tered, though only in minute quantities. 

Spectrum analysis will also play a not less important part in 
the discoveries of elements not yet detected. For if there are 
substances which are so sparsely scattered in nature that the 
methods of analysis heretofore used in observing and separating 
them fail, we may hope to detect and determine many of them, 
by the simple examination of their spectra in flames, which 
would escape the ordinary method of chemical analysis. That 
there are actually such elements heretofore unknown we have 
.already had an opportunity of showing. We believe that we 
shall be able yet to declare with absolute certainty, supported 



by the unquestioned results of spectral analytical methods that 
besides potassium, sodium and lithium, there is still a fourth 
metal belonging to the alkali group which will give quite as 
characteristic a spectrum as lithium a metal which shows, 
with our spectral apparatus, only two lines, a weak blue line, 
which almost coincides with the strontium line Srd and another 
blue line, which lies only a little farther toward the violet end 
of the spectrum, rivaling in intensity and distinctness the lith- 
ium line. 

On the one hand spectrum analysis offers, as we believe we 
have already shown, a means of wonderful simplicity for de- 
tecting the slightest traces of certain elements in terrestrial 
substances, and on the other, it opens up to chemical investi- 
gation a field heretofore completely closed, which extends far 
beyond the limit of the earth even to our solar system itself. 
Since, by the analytical method under discussion, it is sufficient 
simply to see the gas in an incandescent state in order to make 
an analysis, it at once follows that the same is also applicable to 
the atmosphere of the sun and the brighter fixed stars. A modi- 
fication with respect to the light which the nucleus of these 
heavenly bodies radiate must be introduced here. In a memoir 
"On the Relation between the Emission and the Absorption of 
Bodies for Heat and Light " 1 one of us has proven, by theo- 
retical considerations, that the spectrum of an incandescent gas 
is reversed, that is, that the bright lines are transformed into 
dark ones when a source of light of sufficient intensity, 
which gives a continuous spectrum, is placed behind the same. 
From this we may conclude that the sun's spectrum, with its 
dark lines, is nothing else than the reversal of the spectrum 
which the atmosphere of the sun itself would show. Hence the 
chemical analysis of the sun's atmosphere requires only the 
examination of those substances which, when brought into a 
flame, produce bright lines which coincide with the dark lines 
of the solar spectrum. 

In the article mentioned, the following examples are given 
as experimental proof of the theoretically deduced law referred 

1 Kirchhoff, Pog. Ann. Vol. CIX p. 275. See previous memoir. 



The bright red line in the spectr-um of a flame in which a 
bead of chloride of lithium is introduced is changed into a 
black line when we allow full sunlight to pass through the 

If we substitute for the bead of lithium one of sodium chlo- 
ride, the dark double line D (which coincides with the bright 
sodium line) shows itself in the sun's spectrum with unusual 

The dark double line D appears in the spectrum of the Drum- 
mond's light if we pass its rays through the flame of aqueous 
alcohol, into which we have introduced chloride of sodium. 1 

It will not be without interest to obtain still further confir- 
mations of this remarkable theoretical law. We may arrive at 
this by the investigation which will now be described. 

We made a thick platinum wire incandescent in a flame and 
by means of an electric current brought it nearly to its melting 
point. The wire gave a brilliant spectrum without any trace 
of bright or dark lines. If a flame of very aqueous alcohol in 
which common salt was dissolved were introduced between the 
wire and the slit of the apparatus, the dark line D showed it- 
self with great distinctness. 

We can produce the dark line D in the spectrum of a platinum 
wire which has been made incandescent by a flame if we merely 
hold before it a test tube into which some sodium amalgam has 
been introduced, and then heat it to boiling. This investiga- 
tion is important, on this account, in that it shows that far 

1 In the March number of the Philosophical Magazine for 1860 
Stokes calls attention to the fact that Foucault had made already an 
observation in 1849 which is similar to that mentioned above. In the 
examination of the electric arc between two carbon points he observed 
(1, Institut 1849, p. 45) that in the spectrum the same bright lines were 
present in the position of the double line D of the solar spectrum, and 
that the dark line D of the arc is intensified, or produced, if we allow 
the rays of the sun or one of the incandescent points to pass through it 
and then resolve them in the spectrum. The observation mentioned 
in the text gives the explanation of this interesting phenomena already 
observed by Foucault eleven years before and shows that the same is not 
influenced by the peculiarity of the electric light, which is still, from 
many points of view, so enigmatical, but arises from a sodium compound 
which is contained in the carbon and is transformed by the current into 
incandescent gas. 



below the point of incandescence of sodium vapor, its absorbent 
effect is exercised exactly in the same parts of the spectrum 
as with the highest temperatures which we are able to produce 
and at which that of the solar atmosphere exists. 

We have been able to reverse the bright lines of the spectra 
of K, Sr, Ca, Ba by the employment of sunlight and mixtures 
of the chlorates of these metals with milk sugar. Before the 
slit of the apparatus a small iron trough is placed; into this the 
mixture was introduced, and the full sunlight passed along 
the trough to the slit and the mixture ignited on one side by an 
incandescent wire. The telescope was set with the intersection 
of its cross hairs, which were mounted at an acute angle with 
one another, on the bright line of the flame spectrum, the 
reversal of which was to be tested; the observer concentrated 
his attention on this point in order to judge whether at the 
moment of ignition a dark line was visible, passing through 
the intersection of the cross hairs. In this way it was quite 
easy with the proper proportion of the mixture, to be burnt, to 
establish the reversal of the lines Ba a and Ba ft and the line 
K /3. The last of these coincided with one of the most distinct 
lines of the solar system, although not indicated by Fraunhofer; 
this line appeared much more distinctly at the moment of ig- 
nition of the potash salt than otherwise. In order to observe 
the reversal of the bright lines of the strontium spectrum in the 
way described, the chlorate of strontium must be dried in the 
most careful manner; a slight trace of moisture causes the sun's 
rays to be weakened and produces the positive spectrum of 
strontium on account of the flame becoming filled with salt 
particles which have been spattered about by the ignition. 

"We have limited ourselves in this memoir to the investiga- 
tion of the spectra of the metals of the alkalis and alkaline 
earths, and these only in so far as was necessary for the analysis 
of terrestrial matter. We reserve for ourselves the further 
extension of these investigations which are desirable in connec- 
tion with the analysis of terrestrial substances and the analysis 
of the atmospheres of the stars. 
Heidelberg, April, 1860. 



ROBERT WILHELM BUNSEN was born in Gottingen March 15, 
1811. He received his doctor's degree in 1830 and became 
private-decent in 1833 in that University. In 1836 he became 
Professor of Chemistry in the Polytechnic School at Cassel and 
in 1838 accepted a similar position in the University of Mar- 
burg. In 1851 he went to Breslau and the following year to 
Heidelberg, where he remained until his death. Both as a 
teacher and as an investigator, he was one of the most eminent 
of his generation, making many important contributions to 
both Physics and Chemistry. His spectroscope, photometer, 
calorimeter, gas burner, filter pump, battery, etc., on the one 
hand, and his early contributions to organic chemistry, the 
methods of gas analysis, photochemical action, etc., on the 
other, illustrate the versatility of his genius. His work in con- 
nection with his colleague, Kirchhoff, resulted in one of the 
most brillant achievements of the century, the application of 
the spectroscope to the analysis of terrestrial substances, 
which revealed at once several new elements and showed the 
common constitution of all bodies in the stellar system. His 
final contribution was made in 1887 after an illustrious scientific 
career of nearly sixty years. During his last years he was a 
familiar figure on the streets of Heidelberg, in which city he 
died Aug. 15, 1899. 



Brief list of publications of historical importance. 

NEWTON. [Radiation.] Phil. Trans, p. 827. 1701 

PICTET. Essai sur le Feu. 1791 

PREVOST. Recherches sur la Chaleur, Jonr. de Phys. 1792 
PREVOST. Du Calorique Rayonnant, 8 Geneva. 1809 

PREVOST. Sur la Transmission du Calorique, etc., Jour. 

de Phys. de Chim. 1811 

HERSCHEL, W. [Radiations beyond spectrum.] Phil. 

Trans. 1800 

LESLIE, J. Inquiry into the Nature, etc., of Heat. 

London. 1804 

RUMFORD. Memoires snr la Chaleur. Paris. 1804 

DELAROCHE. Obser. sur la Calorique Rayonnant, Journ. 

de Phys. de Chim. 1812 

FOURIER. Sur la Chaleur Rayonnant Journ. de Phys. 

de Chim. 1817 

DULONG ET PETIT. [Law of Cooling.] Ann. de Chim, 

et de Phys. 1818 

HERSCHEL, J. [Spectra of Colored flames.] Ed in. Phil. 

Trans. 1822 

FRAUNHOFER. [Spectra of flames] Gilbert's Ann. 

1823, Harper's Series II. 1898 

TALBOT. [Spectra of flames.] Brewster's Jour, of Sci. 

MELLONI. Sur la transmission de la chaleur Rayonnant, 

etc., Ann. de Chim. et de Phys. 1833-37-39 

MELLOXI. La Thermochrose ou la Coloration Calori- 
que, Naples. 1850 

Ann. de chim. et de Phys. 


DE LA PROVOSTAYE ET DESAINS. [Relation of Absorp- 
tion and Emission.] Ann. de Chim. et de Phys. 1853 
DRAPER, J. [Law of Draper.] Phil. Mag. 1847 

DRAPER, J. [Max, Solar Energy.] Phil. Mag. 1857 

FOUCAULT. [Reversal of D lines.] Soc. Philomatiqne 1849 
STOKES. [Note on Foucault and KirchhofFs Obs.] 

Phil. Mag. March. 1860 

STEFAN. [Stefan's Law.] Wien. Akad. Ber. 1879 

LANGLEY. Researches on Solar Heat. Washington. 1884 
BOLTZMANN. [Deduction of Stefan's Law.] Wied. 

Ann. XXII. 1884 

WIEDEMANN, E. [Luminescence of Vapors.] Wied. 

;, ; ( 1879 

Ann. < 1889 


RAYLEIGH. [Radiation and Molecular Motions.] Phil. 

Mag. 1889 

WEBER, H. F. [Weber's Law A Jftf = const.] Berl. Akad. 

Ber. 1888 

WIEN. [Laws of Displacement, Emission, etc.] Wied. 

Ann. j 1894 

PLANCK. [Law of Emission.] Ber. Deut. Phys. GeselL 

Oct. 1900 




Absorption and Radiation, Relation of .... 40 

Assumption made in establishing Kirchhoff's law . . 76 

Alum, Observation on . . 27 


Barium, Observations on 119 

Bath, Description of 25 

Black bodies, Proof of law of radiation for . . 78 

Bunsen, Biography of 126 


Calcium, Observations on 115 

Caloric, Nature of 17 

" Clausins' " law ',. . . 94 

Cold, Reflection of 7 

Conduction and Radiation, Relation of .... 49 


Diathermancy, Table of 37 

" General 69 

Distance, Law of 9 

Draper's law 95 

Dulong and Petit's law ........ 67 


Emissive and Absorptive power 75 

Equilibrium of heat, Meaning of the 4 


Fluids, Radiant and non-radiant ..... 12 

Foucault, Observations of . ' . . . . . . . 124 



Glass, Observations on . . . . . 26-29-12 


Heat, Conduction of ...'.. . 12 

Absolute and relative equilibrium of ... 7 

" Nature of . . 4 

Helmholtz, Law of . ; . ... . . . 88 

High temperatures, Radiation at 59 


Kirchhoff, Biography of 97 


Lampblack, Use of 26 

Le Luc, Ideas of / . . . 3 

Le Sage, Theory of . . ..,.,. ;. ,. . 4-17 

Leslie, Observations of . 26 

Lithium, on ...... r . 109 


Mercury, Eadiations from . ... . . . 61 

Mica, Observations on . . , . . . . . . 27-29-32 

Mutual Radiations of black bodies . | , . . 83 


Pictet, Experiments of . .... .' . ', . . 8 

Potassium, Observations on . . . . . . 42 

Prevost, Biography of 20 

Principles and Conclusions, Resume of .... 18 


Quality of heat radiated, Experiments on . . . . 33-34 


Radiation and absorption, Relation of .... 40 

" from polished surfaces and lampblack ... 26 

" and refractive power, Connection between . . 42 

*' and conduction, Relation of 49 

" for different thicknesses, Law of . . . . 29-31 

Radiant Heat, Second Series 53 

Radiating Substances, Table of 28 

Ratio between Emissive and absorptive power of ajl bodies 78 



Refractive power on radiation, Influence of ... 42 

Reflective " ' 4< " "... 42 

Reversal of Spectra . 123 

Rock-salt, Observations on 28-30-33 

" Quality of heat radiated from .... 54 

Selenite, Observations on 27 

Sodium, Observations on 107 

Spectral Observations 101 

Spectra produced by spark . 106 

Stewart, Biography of .... .... 72 

Strontium, Observations 011 113 

Swan, Observations of 107 


Temperature and Radiation, Law connecting ... 64 

Temperature of different flames 105 

Theory of exchanges, Extension of 23 

Thermo-multiplier, Description of 24 

Thick and thin Plates, Radiation from . 33-34 

Tourmaline, Radiation and Absorption of .... 95 


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